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ITT: noguns.
First off, caliber does matter, but more importantly accuracy.
I have yet to see anyone ask what type of Bear they are trying to kill, or what neck of the woods they will be in, and what species they will encounter.
Size is relative to the species. An average Black Bear weighs around 300 pounds, a large black wear weighs around 400-500 pounds.
Where as a an average Brown Bear weighs around 500 pounds and can get in to the 1000 pound range.
Calibers I would recommend:
Black Bear: .44, .454, .460
Brown Bear .454, 460, 45-70, 480, 500.
There are a ton of other calibers, those are just fairly common large caliber pistols.
And everyone also failed to mention, if you shoot just about any of these without hearing protection, mainly the 500, you will do extensive damage to your hearing.
Your best best will always be a shotgun. If it were me and I had time and money. I would just buy an SBS (Short Barrel Shotgun), and pay the $200 tax stamp.