Udyr's counters:

Karma - Her slow and her speed up is way too much, extremely annoying against Udyr, buy swiftness and hope for the best.
LeBlanc - The only reason I think she's a hard matchup is because she's almost impossible to gank, if you manage to gank her and pick a kill or two on her though, going to be easy.
Vayne - Hard matchup, if she's any good you will have a very hard time trying to get to her in teamfights but you still should not ignore her.. maybe focus on peeling for your adc or still go for her if you think you can do it.
Vel'Koz - Quite a pain for Udyr, since he can just slow and knock you up all day!
Ziggs - I actually ban him since he's just way too hard for Udyr. A good Ziggs will be IMPOSSIBLE to gank and IMPOSSIBLE to reach for Udyr in teamfights, don't even try you WILL die. Focus on peeling, don't go for him he's going to kite you to death..

BASICALLY:

Your jungle route should be like that:
1. Smite Blue
2. Wight
3. Wolves and smite big wolf
4. Wraiths
5. Red and smite red
6. Golems
There you go, you're level 4 and ready to gank/countergank or keep farming

How to gank:
''as phoenix udyr, when you gank lanes, you turtle, and run in with bear, stun, then switch to phoenix and keep using phoenix, until about 5-7 seconds later, and stun with bear again. you want to keep walking in FRONT of them, since you're playing utility and you'll be faster than them, don't just right click and hope for the best. in teamfights, it's all on your role, as a peeler you want to turtle and bear often, if you're fed and you're just carrying, bear a carry, then just beat them with phoenix and turtle only when you need to.
Zone enemy carries in teamfights (Zoning is extremely important and is the major advantage of Udyr in teamfights, you just run around everywhere peeling and applying pressure on ennemy carries all the time with your stun and your tons of damage) when phoenix comes up, ALWAYS use it. you want to proc that flame breath as many times because it deals so much damage.''

Farm like crazy (you should average 120+ at 20mins, and like 170+ at 30-35mins, even though I admit that in higher elo it gets a bit harder to get to this since the laning phase ends much earlier and games progress faster)

Gank as much as possible without compromising too much farm

Do not gank to apply pressure, gank to kill

When you push towers you should constantly switch stance to proc the trinityforce and kill the tower faster

My name is PopsicleFun and it sounds like a noob but I'm bronze III currently climbing up the Solo Q lader. I main jungle and play any jungle champ. My play style varies throughout the champs I play: Udyr, Lee, Trynd, Yi, Teemo.
I would like it so there is only Positive Feedback only!

Thanks summoners,
PopsicleFun