edit:
Whoa, -2 for daring to be different and trying something that is at least as effective as the sheep build? I don't know when you're supposed to clear jungle by, but I do get an early 5 min clear tanking the long route (which means I kill 3 camps more than just a "clear route") on a very sub-optimal rune set ought to at least warrant not being dismissed straight away, no? I looked up some old guides (pre-jungling + pre-Udyr nerf) saying that a 3:30 clear time is supposed to be the top level. I think I can offer an alternative path that will ultimately be at least as good, if not better.
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I think I just stumbled on something for SR. LF assistant to help finish the build, cuz I suck at jungling.
What this route gives you:
1) A Sheen instead of Mardred.
2) PHOENIX and TIGER instead of turtle.
3) Theoretically a much faster beginner route (A more experienced jungler might be able to start at golem or lizard for the pro route). At any rate, having 2 damage skill instead of 1 makes life rather interesting.
4) Theoretically a much better early burst power.

Current mastery: 0/15/15
Summoner Spell recommendation: Smite + x? (Possibly heal?)
Current rune set: very bad for jungling (I only have utility rune set--note however that I do have slightly higher mana regen than average Udyr)
Starting item:Mana Sapphire+2 hp pot
Skill: Phoenix>Tiger>Phoenix>Tiger
Path: Wraiths(smite the blue one)>pop potion on the way to wolf (you'll level in the middle)>pop potion on the way to small golem, smite will be up just in time for you to finish the last one without dying (Should be much better if you have real jungling runes).
Teleport back, grab 4 hp pots..at least I think you need 4.
Anyway, out to buff golem (spam EVERYTHING as soon as it comes off CD (You have PLENTY of mana) chain chug your hp pot. You will only need 1 on the golem, but it help recover your HP while you're on your way to lizard.
Kill wolves, kill wraiths, kill Lizard (you know the drill), gank or keep on jungling as you wish.

Rationale:
Most Udyrs survive the first few levels by switching into turtle stance, which reduces your damage output. Well, that's all well and good. But the Troll Scientific Institute (TSI) have found that when given extra starting mana, Udyr can power through the first few level of his inefficiencies into his graceful, cheap dance stage, at which point he no longer relies on turtle regen for mana. At least not yet anyway. This is because by level 4, your 2 damage dance will cost 65 each, so that 200 mana you got from your shiny new Sheen is going to give you 3 extra skill cast--4 if you count regen between the time you need to run down your mana to that level.

Additionally, I shouldn't have to preach how Phoenix+Tiger is going to be much faster at killing things than Turtle plus one of the above, yeah?

One of the problem is that I definitely haven't thought through the build after this. I don't Udyr much, and I certainly don't jungle at all. I can't quite tell what kind of item he should be aiming for, but I heard that Triforce isn't a bad one, except that people usually don't build it until the very end. I haven't paid much thought to skilling either. I assume that so long as you hog the blue buff, you'll have more than plenty mana to go around to go Bear. But you might want to start leveling that Turtle soon if you want to remain sustainable without the buff.

Speed is not the only important thing when jungling. You want to have high HP and some mana at level 4 so you can gank successfully.

I run the normal 15/0/15 tiger stance build with cloth and 5 pots starting at golem, and I doubt starting at the wraith with a mana crystal will be able to finish the jungle much faster, and at least not with more HP. The 15 more points in offence and early blue buff will speed it up compared to your route, and are you even able to do it non stop without resting without turtle or 5 pots? To give some credibility to your thread you should at least test it out and show us some results.

Like I told you, I'm running a very sub-optimal rune. I'm running the tests every now and then, but they aren't exactly "good tests", mainly because I don't even remember to Smite most of the time. I know I end (kill Lizard) with 100%mana, but I usually have to run Heal right now (which pushes me back up to 75%HP). I shouldn't have to use Heal if I don't forget to chain chug HP pot properly..(yes, I missed that too). It might also help if I am running AS and dodge runes instead of mana, crit, and CDR. But I'm mainly just looking for some early feedback (and hopefully an experienced jungler to help test the route, because I don't have any runes for it).

Yes, I do take a break mid way through.

Thanks for the feedback. I'll run some more tests and see how it goes.

1. You're lacking starting with a defensive item. If you get counter jungled, you're in bad shape.
2. You're skipping Turtle. Let me re-iterate that in better terms. YOU'RE. SKIPPING. TURTLE. Obviously, you haven't played Udyr enough to underestimate this skill. Its not JUST for maintaining mana, like you so casually point out. Its a damage negator, a lifesteal boost, and one of your best defenses against a counter jungler. Ever been hit by an Eve or Nunu when trying to kill Lizard? I guess not, if you're ignoring Turtle.
3. Smite + Heal? How do you catch up to your target when ganking? Bear alone is not enough, I can assure you, unless you have superb teammates with good CC. And how do you escape teamfights or bring down runners? Udyr is melee, and HIGHLY susceptible to kiting. No Ghost/Flash = useless Udyr.
4. Early mana crystal might make double offensive stance possible, but the lack of Madreds will GREATLY slow down your jungling after about level 4-5 and hugely increase the time you need to kill Dragon / counter jungle enemy buffs. Lets put it like this: You're a jungler, you need Madreds Razor. Thats it. There is no discussion there.
5. Without Turtle, you're ganking is riskier. Ideally you should be ganking at an advantage but that's not always the case. If the enemies you're ganking turn around and fight, and kill one of your lower health lane friends and turn on you, you're in SERIOUS trouble without Turtle. You have no defensive ability whatsoever. If you go up against, say, a Jarvan-Sion combo, you're in deep **** unless your own laners are equally strong (and even then its dangerous, as the enemy will target you first to deprive you of buffs).

tl;dr Big difference between theory and reality. Give jungling a serious try for at least a number of games in a row, get some appreciation for Madreds Razor and Turtle Stance, then come back and discuss this build. I guarantee you yourself will write it off.

Thanks for the input, Aemon.
I can't say that I know how to play Udyr, or jungle. So yes, I think I might be underestimating Turtle in that regards. I'm usually the roamer, killing junglers, so I don't quite know what it feels like to be on the other end of the stick.

Anyway, just updating the result.
I'm still using the support runes and defensive masteries.
I still can't find a way to bring down big golem without using Heal. I heard that a proper build can do it with long sword, so clearly there is a way to do it without cloth armor and only 1 pot (I have no idea how though). After that, I still need to B after killing the wraiths, get 3 more pots, and run through the route. I forgot to use the pot and Smite on Lizard (again), leading to a much lower finishing HP than necessary (50%HP, full 30% mana) with total clear time of 4:15. I'm thinking of trying to start at small wolves next time to save that initial 30sec while I wait for Golem to spawn. Should be able to save 5 to 10 seconds that way. Forgot to check my gold though, but I assume there should be just enough for Sheen.

I'm going to give dragon a hard thought. Like I said, I was only concerned with jungle clear time at this point, so it totally skipped my mind. I suppose that with Turtle, it's very much doable at level 4 (?). I'll see when is the earliest time I can pull it off with Sheen. Supposedly though, Mardred should be able to give 500dmg at around 15% chance, or every 7th attack, depending on your luck. I think the best that you should be able to pull would be 2.0 AS by that level (can't say for sure), so maybe once every 4 seconds. If I stance dance between the two stances, I should be able to proc Sheen once every 3 seconds for a measly 40 dmg, and maybe add 2-300 damage from using Phoenix, and maybe an extra 30-40 on Tiger proc (AD bonus) instead of turtle, so advantage Mardred there, but I don't think it will be that much better (damage-wise).

Conclusion so far--at least as far as basic clear time goes, I think there is no disadvantage in going double damage. However, I do see that the traditional build is probably going to be better once you start doing dragons.

I posted tyhis yesterday in the competitive play forums but it seems you guys would like a decent read. As Aemon was saying if you dont start out with one of the items to make a razer no matter how fast you are in the begining as soon as the other jungler has a razer youre going to be significantly slower in the jungle. Also i disagree with Aemon on the needed turtle to gank TURTLE DOESNT DO DAMAGE who ganks with in a def stance maybe switch into it before you get there for the shield but you def want to bear/cat for ganking ofc you want to used it while running away but you should put yoursef in a position to need turtle to kill have your laners initiate and run in shouldnt take much damage and when you get a wriggles if you play ad like myself the lifesteal in the jungle from that and tutrle will heal you from some minor damage you take while ganking.

Red:
3 Armor Pen (5 Armor Pen) (Greater Mark of Desolation)
6 flat AS (10% AS) (Greater Mark of Alacrity)

Yellow:
9 Flat Armor (13 Armor) (Greater Seal of Resilience)
Best way to redude the amount of flat damage in the jungle. I tried that dodge and it felt like it was completely random if I get raped or take 0 damage so for a more consistent result use armor. Plus all the jungle creeps do physical damage.

Blue:
CDR @ 18 (8.10%) (Greater Glyph of Celerity)

Imo most of the blues suck for junglers you can pretty much use whatever you want. MR @18 is decent ends up being something like 24.

Quints:
3 Armor Pen (10 Armor Pen) (Greater Quintessence of Desolation)

[COLOR=#063677]http://www.mobafire.com/league-of-le...:6-262:9-267:9[/COLOR]

I use 21/0/9 although Ive been using 20/0/10 because if you think about it 5% damage ******* blows. Infact 5% less damage ******* blows too. You'd have a be hitting like a supersonic train for 5% damage to even count, 50 extra damage on 1000 damage hit LULZZZZZZZ who would get that. vice versa for 5% reduced damage. I put the extra point in Utility Mastery extra buff duration is nice, more oppertunities for ganking with dubbuff and it helps you clear the jungle faster. You can also use that page for pretty much any jungler, the only jungler i have a special page for is shaco because hes really soft.

Build:

The build really varies depending on the team comp you're fighting its pretty much on you to make the calles from here but I' ll tell you what I do.

First you start off by getting a long sword and taking cat stance. Run to mini golems and kill them you'll hit level 2 from them. you can buy a potion if you think you will die... don't worry they will never kill you unless a. you **** up or b. they gank you hardly ever though just pay attention to the map and alter your route depending on whats going on. Once you kill golems recall back and get 3 healing potion and a mana potion. run to blue if you don't think you'll need ghost in the next 3 mins then use it to run to blue then its smooth sailing from there just do your normal stance dancing Udyr.

Items: rush razor then get boots morph the razers to wriggles get merc treads after that be sure to farm just a little extra gold before you return so that you can get wards or pots as needed. After that its your call on either brutalizer or sheen either one works well more burst comes from sheen more dps comes from brutalizer. youll always want a tri-force. At this point is when you get to get a defensive item or two like ive been saying depending on the situation you may only need 1 or you may be the teams tank. As far as survivability goes tutle is pretty nice tool to use just spam it and bear and run lol. Id recommend counter build the enemy team and build to your play style. You should should develop your own way of playing that way you will get ideas for other champs broadening your horizons as far as playing field looks.

@ Expedio: Your post looks solid you may want to try out other masteries. I personally think that the defensive masteries are for the jungle phoenix (as and ap mastery in def) IMO it is inferior to cat and offensive masteries because you move a lot faster through the jungle and when you gank your damage output is much greater then that of defensive/phoenix. But this is a matter of play style. /salute

Discussion: On the phoenix passive every X amount of hits you proc 40 extra damage. I cant remember the exact amount but i think its 3-4. If you take 1 point in it at 5-7 you can get some extra damage and you wont even have to change into phoenix stance i havent done enough testing to see what i like better or what is in fact better with math but you guys tell me what you think about that 1 point in pheonix. skill order would look something like this: Q>W>W>E>Q>R or Q>W>W>E>R>Q ive yet to try it but Q>W>R>W>Q>E would give you the really fast extra 40 damage on x hits with no mana you have to spend for it. As Udyr players we know his skills get exceptionally better with each point in them so Im not sure which is why I decided to post it here.

Note: In my masteries i do not take the 10% more crit damage mastery instead i get more damage to creeps and max out cdr as and arp

I don't understand what you are saying here. Can you proc phoenix damage without changing to phoenix stance?

I have another question too. If you change straight from phoenix to tiger and hit, will the AD bonus from phoenix boost your tiger stance DoT? If so, it seems like a pretty strong gank opener. Phoenix->Tiger->Bear should be the strongest initial burst.

(Stance) - Activation: Udyr sends out pulsing waves of fire dealing magic damage each second to nearby enemies for 5 seconds. In addition, during this time Udyr's ability power is increased and his attack damage is increased by half of that amount.
Persistent effect: Every third attack, Udyr engulfs the enemies in front of him in flames, dealing magic damage.

Cost: 75 / 65 / 55 / 45 / 35 Mana
Waves' Magic Damage: 10 / 18 / 26 / 34 / 42 (+0.25 per ability power)
Ability Power: 16 / 24 / 32 / 40 / 48
Attack Damage: 8 / 12 / 16 / 20 / 24
Third Attack Magic Damage: 40 / 80 / 120 / 160 / 200 (+0.25 per ability power)

yes to if you take 2 attacks and then run in for a gank, youll get the extra 40 damag from the 3rd hit, its no mana and is passive thats why i brought it up to see what other udyr players think. I havent done enough testing yet to tell you guys what is better but it seems to mee that 40 magic damage on top of a cat proc can be almost overwhelming for some early game champs.

don't you lose phoenix persistent effect when you go bear stance for gank?

You have 5 seconds to do it. Reading skills does wonders.