I don't think some of you people realize how fast these critters can be. Bears are like crazy fast defensive ends--their ability to cover close distances very fast is exceptional. At the ranges most of these encounters occur at, only having 6 rounds isn't going to matter because you'll be lucky to get half of them off before the bear is on top of you, esp if you do any aiming to make them count.
I've seen black bears casually lope sidehilling at 25+ mph next to my truck. At close range, a grizzly can chase down a horse. If you aren't situationally aware enough to catch the bear before it is within 40 yards of you, and it sees you before you see it, you'll be lucky to draw and get a single round off--that's how fast these animals close distance.
So if you only have one or two rounds to get the job done, it makes sense to make them as effective as possible. If it keeps you from going unarmed completely, a handgun will have to do. I carry a Glock 20 loaded with full power 10mm, which is ballistically similar to full power .357 Mag. While I consider this adequate for two-legged predators as well as cougars and possibly black bears, I never considered it proper grizzly medicine, and that is just the lil' guys we have in MT, not the big bruins they have in Alaska. Handguns are convenient, but they are marginal at best in skilled hands against aggressive bears. I'd rather have a .338+ caliber rifle, or a shotgun loaded with Brennekes.
If I had to load a handgun for bear, my choice would be a 4" Ruger Redhawk .44 Magnum with some 300+ gr hardcasts. This would be about the most I could hope to get accurate follow up shots off in with any sort of rapidity. I'd aim for the head/upper spine bear the back of the neck and the shoulder hump. But more than likely, even then, against grizzlies, I'm probably not even drawing unless I have a longarm.
Drawing on my military experience, were I to encounter a large enough bear, I would try for a
"mobility kill"-aim at a hind leg and slow it down enough that I could run away.
If you get a shot at a bear's hind legs, chances are it's already facing the right direction and you don't need to shoot it. If a bear is coming at you, the hing legs are going to be an even more difficult target than its head.