Anti-material rounds like .50 BMG are way overkill for anything you'll find in North America, calibers in the .338/.375 range, with around 1/3 the weight and energy are probably good enough (would have to check for bear, my family's never hunted them and none are to be found in my home town). For "thick skinned" dangerous game in Africa, heavier stuff is legally
required, but the energies are still quite a bit lower than .50 BGM.
Hmmm, while it gets into "destructive device" territory ($200 Federal "tax" per round and of course paperwork, which they aren't exactly required to accept), something that explodes with a fuze that sets it off way before it nears the ground is called for. You want proximity fuzing anyway ... send a microprocessor after a bundle of them wrapped in an airframe ^_^.