i have run DPS udyr quite a bit, and very successfully I might add. The key to it is stacking ability power and attack speed rather than damage for Tiger Strike. Remember, Phoenix strike activates on every 3rd attack, so AS is important to make sure you get in 3 attacks before switching stances. Here's the Build (details follow)
Ninja Tabi (to stack with Monkey dodge)
Guinsoo's Rageblade (Damage, AP, AS... what's not to like?)
Nashor's Tooth (speeds up stance juggling by a full second!)
*Hextech Gunblade (the spell vamp will heal you completely in one creep wave
**Lich Bane (makes Bear much more effective)
***Randuin's Omen (CDR, slow, Armor, HP)
*If a team stacks magic resistance to counter you, sub Malady for Hextech. If you're playing against another jungler (WW or another Udyr) sub Wriggle's Lantern for Hextech.
**Build Lich Bane only once you have more AP than AD, otherwise Sheen > Lich
***Sub Banshee for Randuin if you find yourself being disabled too often.
The nice thing about this build is that (with the exception of Guinsoo's) all the items have cheap intermediate step items for the early/midgame. This is very important because you'll rarely make enough gold jungling early game to buy pricey items like Giant's Belt (which is why I do not recommend RoA rush, Rylai, or Warmog). My start is usually Doran and a Mana pot. I usually buy Tabi, Sheen, HoG, Bilgewater, Nashor, Guinsoo.
Before you have Guinsoo, Tiger will be your most potent attack. Once you have Guinsoo, your attacks should go as follows: Chase with Bear (for stun & Sheen), Tiger ASAP after Bear (to stack guinsoo), then phoenix for a massive Sheen + Guinsoo AoE. If your opponent (lunch) tries to run away, Bilgewater/Hextech/Randuin/Bear. If your opponent (lunch) engages you, Randuin/Turtle. In either case, it's back to Phoenix. Rinse, wash, repeat. Remember: always pop items before returning to a stance other than Phoenix or Tiger (i.e. hextech > bear ; Randuin > Turtle) because they will start a CD on your two main attacks.