I like to solo lane push..while the entire team is busy fighting one side I sneak to a different lane and push it far in, I tried udyr focusing on phoenix, bear for running (hit bear, stun champion who came to anti-push, run), and one in tiger for the attack speed while destroying towers, summoner spells were teleport/promote...Yet when I finished the match I noticed I had the least minion kills, a lot of assist kills, and only a couple towers :/

What could I do to be better? Are any other champions better for this?

inb4 flamed for not helping team push the lane they push

AP Yi is probably the fastest pushing champion in the game,
however, its up for debate how viable he is in a match

Just because you are trying to be a backdoor champion doesn't need you don't need farm...

ALWAYS work on last hitting, farming open lanes, picking up jungle creeps (if you're jungle you should be farming any time you're not actively ganking a lane or covering a lane from being pushed). Regardless you should be getting high CS regardless of choice of backdoor character.

Split pushes work great but your team really needs to be able to hold their own without you. If you have a reasonably tanky team or one with good poke just wait for a stalemate over a tower and go push on of their lanes. They'll have to send at least 1 person to counter the push, you then teleport back to allies and help them clean up the weakened enemy team (down 1-2 people)

Im confused, so what is your recommendation of champion?

And no, they send someone to counter me, I either kill them (though being built as a minion killer it usually is not so), or run, once they lose me I either go back to that lane or go to a different lane to backdoor.

I asked for a good backdooring champion, not a good backdooring strategy,

Twisted Fate with Teleport for solo-pushing lanes. Teleport+his ult allows him to stay two steps ahead of the enemy team, jumping across the map with teleport to solo-push a lane and then gating to safety if enemies come after him.

If you are looking for a good back dooring champ here is a list of some champions you might like to try but it depends on your play style as to what the "best" champion will be.

Solo top: Tryn, Yi, pantheon and possibly Irelia
Mid: Kennen or Twisted fate
Bottom lane: Sivir

Basically you want a champion with a good escape mechanism and damage. You might be surprised why I choose Irelia but I choose her because back dooring usually occurs towards late game and that's when Irelia becomes very strong and durable.

Teemo is a strong split pusher, mobility + fast minion kills + free shroom wards means he's got te most outright utility. Nidalee is another strong split pusher, if built right.

Shen is an amazing split pusher in the right team- and by right, I mean you have someone else on your team who can initiate fights (that you then ult into). Also quite good on poke teams.

Yi is probably the fastest tower destroyer in the game, at least that I've seen. His ult + ghostblade and the towers will literally melt. Late game you can actually just walk up to it without minions and tank it, and kill it, without the enemy being able to respond fast enough to do anything about it.

As a rule of thumb, a split pusher needs
1- to be able to push fast and hard
2- a quick escape mechanism, and good mobility
3- to be either non-pivitol in a team fight, or able to get back to the team fast enough that you can't tell he's gone (Shen, TF, Pantheon)

Also an important ability is to be a good dueler.
If the enemy team is forced to send two people to stop you because just one would get killed, then it's great for your team.
If the enemy team can stop your split push and kill you with just one champion, it's usually pretty stupid to be trying to split push in the first place. There are exceptions, of course. Like if that one champion that can stop you is a critical part of the team fights, and your 4 teammates can steamroll his 4 teammates in the absence of you two.

But in general, better duelists are better split pushers. For example, take Karthus. He can push really well and can impact a teamfight from anywhere on the map with his ult. But he's (usually) squishy as heck and is a lousy at 1v1, so if he split pushes at the wrong times, it's very easy for him to get caught and killed by many champions. Ones that can hop over his wall, at least. It's pretty easy for him to escape from champions without any dashes because of the retarded slow on the Wall of Pain.

Jungle yi with ghost is the best option i've found. Wriggle's -> Zerker's -> Youmuu's -> Phantom Dancer -> Thirster -> Whatever you need. The build is kind of flexible. You can get boots of mobility if they have someone like shyv, udyr, or someone good at chasing you down and getting you in the long run, or someone like TF who can cross the map quickly. But I've found that I can 1v1 anyone once i get brutalizer (i usually run ad carry runepage, but sometimes i opt for attack speed. both work), so I can always hold my own when they come to gank me. And once i get brutalizer, i can take down a turret from full to nothing in roughly fifteen seconds. And then I escape with ghost if i have to.

I won't even bother explaining the champion. Just play AP TF mid with teleport, get a deathcap and lichbane, and run around 1-shotting minion waves and eating towers. You'll see why he's split push king.