Dominion is all about capturing and defending captures. With this build, you are going to die quite a bit, I usually end up dying 5-10 times in a game (mostly at the end). But it doesn't matter, because there is hardly any effect at all from feeding in Dominion. You are going to be able to kill enemies fast, but killing is not your main objective.

Mobility is key for Udyr in Dominion. You should constantly watch the map so you see where enemies are heading. Then you pop up at undefended points and steal them. If you time it right (usually when enemies is about 1.5 points away), you will have turned the point just when opponents turn up, and you should easily kill one or two of them with the help of your new turret.

After a fight, run around the edge to pick up healing boosts, using the speed buffs, and constantly keep an eye on the map to see where your next capture could be.

Using that strategy only, you should end up in the top 3 in every fight, around 1100-1600 points depending on how long it goes on for.

Armor penetration marks will help you kill things faster.
Armor seals will help your survivability a bit. You might want to take dodge instead.
CDR glyphs is so you can take full advantage of your skills.

Masteries is going to be a bit of a mix and match. You will want cooldown reduction from the offensive tree. And you will want some armor and magic resistance from the defensive tree to increase your survivability. Then you want the movement speed buff from the utility tree.

Items are heavily focused on movement speed. With that, you get some life-steal, some attack speed, and some armor.

Mobility is always number 1. You may want to change the purchase order a bit depending on what champions you face. For example, it may be a good idea to get Phage first of the trinity items, but in other games it's better to get Zeal first for the speed.

Sanguine blade is something that would fit good here if you want to play around a bit.

Always take a point in bear stance to begin with, so you can stun enemies. Then focus on tiger stance.

Phoenix stance can be good if you have time to push for a capture point. Then you level that to kill minions fast and get your own minion wave with you for a point capture. However, if the opposing team is capturing points faster than your team and picking up a lead, you should focus more on finishing bear stance early, so you can move around faster to those unguarded points.

If your team is set on only defending 3 points and not capture any more, then you should level turtle stance earlier so you are better able to go into defensive mode at the turrets.

Ghost
Exhaust
Flash
Ignite
Revive

Any of those is a good pick. Some people really underestimate the power of revive in Dominion. When you revive, you will have a speed boost that will throw you to the other side of the map in an instant, able to capture an undefended point by yourself. But revive is on a really long cooldown, so it may not be the best pick if the fight is short.

Move fast, capture fast, kill fast, leave fast and go to the next point. Works well for me. Try it out and let me know what you think.