Not sure who brought this back to life, but it was a bad idea. Way too much bad information.
The OP never answered the question how much experience he has with firearms. Still not convinced the guy could safely handle a gun.
Someone that sees a bear behind every bush, could be a danger to others.
I've spent 33 years in Alaska, been around black bears, grizzlies, and polar bears. Grew up in the western part of the country and not been at serious risk. I've been in South Central, the Alaska Peninsula, up and down the Yukon River, in the brooks range, Kotzebue, Nome, Barrow among a lot of other villages and never had to actually fight one off. Don't get me wrong, I've seen plenty,
Don't get me wrong I've been so close a few times that I had my gun in my hand, just in case.
You don't really need to shoot the heaviest, fastest, hard cast out there. Bears are thin skinned and moose have heavier bones. Have I killed a brown bear, yes I have. I went looking for him. Do I carry a handgun, just in case, but I've been shooting for well over 50 years, with everything including the 357 mag, 44 mag, 45 Colt, 454, and 480. Last one I'd carry is the 454. For one thing, it's not necessary. For another I know two different guys whose heavy bullets, pulled during shooting at (DLP) bears that have gotten too close, and for another, they aren't necessary.
Guessing the guy could go looking for one and not even find one. Which is the goal for him anyway. As Contender said, go through 3-4 big cans of bear spray, putting the clip on. Take it off and spray, then do it again. Do it over and over. See what it's like to get overspray in your face. Learn to think on your feet.
Rant off. Sorry if I offended, don't be so sensitive. We're family here. I can say for a fact, Polar bears are much more risk.
Someone brought up cougers (mountain lions) they can easily be killed with a 38 Special, if that's an issue. Not really sure what else to be afraid of. You are certainly at a greater risk just getting lost, so keep some survival gear attached to your body. By the way , when is the last time you've started a fire with just what you carry in your survival pack or on your person. If you are going to get out there spend some time thinking about that.
If you really want to get a butt pucker, have a plane drop you off in the bush and fly off, then wonder if he can find you again, especially when he's a day or two late. Happened to me 2 times. One was severely late. Considered shooting the pilot, but the fact that I can't fly saved his life.