I have never shot a bear and don't claim to know anything about them so take this for what it's worth.
I have had to euthanize some cattle over the years on the ranch for one reason or another. It's not something that I enjoy doing, but it is part of ranching. I have learned that the minimum handgun that I am comfortable using is a 4" barrel 357 magnum and a 158gr JHP or preferably JSP of reasonably stout construction. Those will penetrate the skull from any angle every time. An older bull or cow has a pretty stout skull.
I'm fairly sure that if I had Buffalo Bore or similar ammo in my 9mm or 45 instead of FMJ I'd have seen better results penetrating bone. I never planned to use the semi-auto guns, I just ended up in a spot where they were what I had at the time and needed to end an animals suffering. The frontal shot didn't break the skull either time, but did stun the animal enough that I could get in position to place a shot behind the ear pretty quick. After deciding I would only use the 357 I started carrying one in each of my ranch trucks. The 3" barreled S&W 60 failed to penetrate the skull first shot once on an older cow with the 158gr ammo, so I quit using it also. I assumed it just didnt' have quite enough velocity in the short barrel, but it could have been a freak deal. Either way this is a job I want done as painless as possible so I'm sticking with what I know works. Since going to 6" Ruger Security Sixes I found reasonably priced at pawn shops in both trucks I've went years without an issue. I won't ever go lighter again. It's an unpleasant part of my job to have to end the suffering of our stock and when it is necessary I want to do it as quick and painless as possible.
I just wanted to share my experience. It's a different animal under far different circumstances, but it's still penetrating bone with a handgun.
I do hunt in black bear areas and have plans to hunt in grizzly areas. I carry a handgun when scouting and sometimes when also carrying a rifle. I'm currently using a S&W 386XL Hunter in 357. It's just over 30oz, as light as the 4" Ruger SP101 it replaced. It is a full size 6" barrel 7 shot revolver that I can shoot well. I grew up putting bricks of 22LR through a Ruger Single Six and when I draw a revolver my muscle memory has me cocking the revolver in the process. The 357 puts my thumb in the right position to do this. I have a Ruger Redhawk 5.5" 44 magnum that is just a little to big a revolver for me to do this as quick and smooth. It's a great revolver and I can shoot it well just not as fast. I had my gunsmith smooth up the trigger and install Meprolight Tritium night sights on it to make it a great sidearm for bear country. Practicing with it I just can't put the first shot on target as quick or reliably as I can with my 386. I don't have huge hands, I wear a L in most gloves. I put the Redhawk on Gunbroker recently. I shoot 1911's quite a bit and may end up going to a 10mm 1911 at some point, but I don't know. They are considerably heavier than my 357 and I don't know that I'd every be quite as quick and accurate as I am with the 357. I don't shoot striker fired handguns as well as I do 1911's or revolvers with their crisp triggers so I'll stay away from the Glock or new Springfield XD 10mm. I spend to much time shooting rifles with 2lb triggers and just don't do nearly as well with the long spongy triggers on striker fired autos.