It's a bit overkill for a bunny, and that is providing you can hit one with it. Not to mention riding a dirt bike with a handgun?
If you want to go rabbit hunting, go rabbit hunting. Are you afraid the little bunnies will jump up and knock you off from your bike?
Most use a shotgun for rabbits, but you can do it with a rimfire as well.
I'm not sure it would be legal either, deffinately might want to check into that.
Paul