There is hunting, where the hunter generally knows more about the situation than the bear (hopefully) and has the advantage.
Then there is stopping, where the bear is more up close and personal--and irate and coming at high speed.
Art is spot on here. I think people don't make the connection that there is a difference between hunting and self deference.
People(including my self) hunt bears with archery gear. Would I want to defend my self with the bow? But I would hunt with it.
I think most any quality well constructed medium caliber and up bullet would do fine in a hunting situation.
However, in a self defense situation the fattest, heaviest hunk of lead that you can push the fastest is what I would want.