After living many years in the Alaskan bush, in Polar, Brown and Black Bear areas I have a couple of comments. By the way, this comes from one who has killed over 30 Brown Bears in self defense. Just so you know, the difference (at least in Alaska) between Brown and Grizzly bears: They are the same species, but Brown live close to water and catch a lot of fat fish, Grizzly live inland and eat whatever they can find. The diet of the Brown makes them really big, but a bit less aggressive. While the diet of the Grizzly makes them smaller, tougher and some say meaner.
We used to joke that the only defense one needs is a single shot pistol. Just as the bear is about to sink his fangs into you, take the pistol and shoot yourself in the head - problem ended.
There are places in Alaska where one needs to carry a firearm at all times. I mined for a number of years and we didn't go to the outhouse without picking up a rifle. Everyone has their favorites: Indians will be the most likely to carry a 30-30 carbine, Eskimo's are more likely to carry a .223 semi-auto. By the way, they get away with these weak rifles because they may very well be the best shots in the World. The janitor at a local school killed a Polar Bear with a .22 rifle. He used about 90 shots. He would come in close on his snow machine, fire the rifle and then move off to reload.
White men in the bush hardly ever carried anything smaller than a Winchester .300 mag. Guides usually carry .375 H and H mag - this is just in case they need to dispatch a wounded bear. The most popular caliber for non-natives to use is the .338 mag, my rifle of choice. My ex-wife carried a .458 Winchester mag - and yes she could fire it and do it well.
I've used a 12 gauge shotgun on a Brown Bear with success. I used rifled slugs with the last shot 00 Buck. My theory was that if I was not able to kill the bear, at least I could blind him so I could get away and reload. The shotgun was not and is not my first choice. The energy of a 12 gauge at close range is just about equal to any large bore rifle. The problem is the "close" part - very close.
Once, three of us were cooking dinner on a gravel bar. A Brown came running down the hill charging us. We later counted 35 shots had been put into the bear. The bear did not die at the scene. He howled all night long, walking around our camp in the dark. When first light came, we went after him to finish him off - we never found him. With all those shots, he still was able to get pretty far away.
I did use a pistol, .44 mag, to kill a Black Bear. It stepped through the large window in our cabin. Our bear rifle was kept next to the door (on the other side of the bear), my brother woke up and said, “Christ there’s a bear in here.†With that said, the bear focused on my brother. I pulled the pistol from under my pillow and killed the bear - one shot.
There is a difference between a bear hunting you and you hunting the bear. When the bear has its adrenaline pumping and is attacking, one needs a “big stick.†If you are hunting the bear, one shot is usually all it takes. The drill is to aim for a vital area, shoot, and then sit down and wait about an hour. Usually the bear will, if still alive, run/walk a short distance away. If he sees no one chasing him, he lies down and expires. So I’m told, for I’ve never gone bear hunting.
Almost everyone living in bush Alaska, with the exception of those who work for the Park Service, will also carry a side arm. Most old timers will tell you that they will use the pistol to try and frighten the bear away. One never wants to use a valuble rifle cartridge for this purpose.
Good god, I didn't realize how much I wrote. Now it's past my bedtime.
Good dreams,
Frank
). I have been stupid (not brave) too by carrying a pistol in bear country or relying on someone elses pistol. It's better than a sharp stick or screaming like a girl! 
Everything's a compromise, sort of like motorcycles! 
