I hunt bears every year here in Co., I should say I buy a license every year, to have during the elk season, in case I have an opportunity. I've been close a dozen times but no shots YET. I asked our local Game Warden about legality of taking a gun to follow up on an arrowed bear. She said sure it is a constitutional right to bare arms. But you can't shoot the bear with a gun unless YOU ARE BLEEDING.
My experience is that bears run away....