In Michigan if you have your concealed carry permit your can carry during bow season. That said, you had better let the bear bite you before you use a firearm on it out of season.
Honestly though, I've had a LOT of close encounters with bears, big boars, mommas, mommas with cubs you name it. I could fill a whole evening telling bear stories and I've never had one act aggressively toward me. They've bawled at me and tore trees down around my stands when I wasn't there but they always have backed off before I ever felt overly threatened (adrenaline rush notwithstanding).