My go to firearms in a survival situation will be a Ruger Combo: Mark II pistol and 10/22 rifle.
In a survival situation you will not have access to any means of keeping large amounts of meat from spoiling unless you plan on smoking the meat to preserve it.
That said, you will be looking to fill the cooking pot on a as needed basis. The .22 LR will drop small game with accurate shot placement. .22LR ammo is cheap. Think about it, would you rather move 1000 rounds of .22LR or 1000 rounds of say .357 or .45ACP ammo. Two bricks of .22LR in a ruck is not that noticable. Also, the report of a .22LR is less noticable than one of the .357 / .44 mag hand cannons.
I know that this thread started with the bear threat as part of the situation, but why worry about bears if the are not native to the area that you live. I plan on being at the top of the food chain if I have to run for the hills.
Ammo and camo will keep you at the top.