(you need about 4,000 lb. ft. of energy to kill a bear, most handguns have around 400 lb.ft. for, say, a .45 - ineffective)
Being as this is an area of interest of mine I've got a few points as an aside to this statement. First the biggest factor in lethality in a shooting is always placement. Bear, deer, or person the bullet placement is the most important single thing. That being said there are certain issues with bears in particular. normal self defense ammo is designed to use on people and is designed to penetrate to a particular depth to achieve the most damaging result. When you shoot a bear you want better penetration to optimize the lethality of the ammo. So both shot placement and ammo choice is more important than pure power. As to the .45 400 ft lb is a bit low but in the area but you can get ammo that is over 600 ft lb and if you are very skilled and shoot it much better than anything else it may very well be the best personal defense weapon for a particular person, tho not what I would use. I have to say the claim of needing 4000 ft lb to kill a bear is a bit strange when you the talk about carrying a 12 gauge. Much more powerful than a .45 but it normally is only about 2500 ft lb's itself. There was a hiker in 2010 that killed a Griz in Denali with a .45. He fired 9 rounds and the bear was found about 100 yards away from the shell casings. luckily for the hiker the bear fled before succumbing to it's wounds because it may have made it to the hiker but the others with the hiker would have been saved regardless. There are issues with using a 12 gauge also tho that seems to be the automatic "bear gun" reply anytime the question comes up. Buck shot just doesn't penetrate very deep and both buck and slugs loosed force quickly with distance. The "best" bear gun would of course be a high powered rifle but in self defense situations you have a lot of additional factors. One is that the bear needs to be close, within 50 yards, for self defense can really be claimed as a necessity. The gun would also need to be with you at all times, quickly deployable, and something you can move with in brush and quickly acquire a close target with. That would be a benefit to a shotgun as well as the familiarity and comfort many find in it's use but by the numbers a camp rifle in a heavy pistol cartridge would be better if you go by the numbers and something like the .444 or the old 45-70 would be a great choice.