The 2nd admendment right gives you the right to carry a sidearm while bowhunting wether or not the regs say so. As long as there is no bullet hole in the animal they can only sight you for carrying it.

I've seen alot of bears hit with rifle and bow and they don't always go down right away. And as far a bear bleeding out while he's attacking you remember that a bear heart rate is really slow. Thus meaning you could be in a bad situation. I always pack a sidearm in the woods regardless hunting or not. Not going to be a snack because I didn't think it could happen to me. Read the book Ghost Grizzlies and then think about it.