The mayor of Barrow carries a .44mag under his coat for defense against polar bears, especially in Winter when they have a strong tendency to come into town to hunt the only available food (residents). I haven't spoken to him in a while, indeed, I don't even know if he's still the mayor, but it was my impression that it was the old reliable S&W with the long barrel. Under the coat to keep the oil oily, and not frozen. He rides a bicycle to work, even in the Winter. Polar bears are one of the few animals that actually have a tendency to scare me...they are DEFINITELY nothing to fool with; they're smart and mean, and agressive. If a .44mag would do the job, that's what I'd use.
Probably the BEST weapon I ever saw for use against dangerous game was a machan pistol. It was British, for use by tiger hunters in India. This is the type of hunting in which a bait animal is tethered out in a clearing and the hunter(s) wait in a platform (machan) built in a tree, and shoot the tiger with a rifle while he's busy eating the bait. Apparently, this was not always a successful idea, and sometimes the tiger would take it into his head to investigate the area more thoroughly, thereby coming upon the machan and its occupant(s). This was not considered funny. Tigers are very tall when they stand on their hind legs, and they can jump like crazy, like all cats. Ergo, a defensive weapon was needed that could be more readily deployed at close quarters than the rifle. Hence the machan pistol. The one I saw was built on a double-rifle action with about 10" side-by-side barrels. Pistol grip about like a dueller. Caliber .577 Snider (the old British Military rifle round). I understand it kicked like a mule, but pretty much destroyed anything in front of it. Sounds like it might be good for bears. The punishment to the hand would be compensated for by the effectiveness of the hit. IF YOU HIT!