Can Udyr get a base mana regen buff

No. Uydr spamming his spells like crazy and not thinking has been a problem for a year. Finally the cheese is getting killed off.

If you are really having mana issues, consider getting a Tear of the Goddess since Manamune is a good damage item for Udyr.

Otherwise, just stop acting like you still have Spirit Stone and be more conservative with spell use. Phoenix Udyr only really needs 1 W and 1 R to clear camps pretty quickly and he should get most of the mana back from the camp.

Note that you shouldn't have mana issues if you Ranger's Trailblazer as your smite upgrade and/or if you get Trinity Force and Frozen Heart after Devourer