RE: Bow black bear
Is it legal? Well to my knowledge, there are no bow-only spring bear seasons. Spring bear is an any weapon hunt. It's fine if you chose to hunt with a bow for the extra challenge, but there will be other hunters in the woods with rifles at the same time since there is only one spring bear season. If you want to bring a gun with you, that's fine.
If you are talking about hunting bear during the fall archery season however, I'm not completely sure. I think with most states you can carry a pistol during archery season for self defence, but you can't use it to finish a kill after initially shooting it with a bow.