In Virginia if you have a concealed permit you can carry during archery season.
As to a handgun for backup on bear. I would choose a double action revolver in at least .41mag for blackies and .454 for griz's. I would want a short barrel and practice, practice, practice.
If you get jumped by a bear there is a mighty big chance he will end up on you. In that situation when you are pushing the gun into the bear/cougar/rabbid possum

there is a chance a semi-auto would not fire. You could put a revolver's barrel into the ribcage as hard as you want and it will go off.