OK, I'll play.
I'm happy with a 1911 Colt for the black bear we see here in Colorado.
Many years ago, Jeff Cooper mentioned a little book that Colt published in the 1930's. I found a copy in a collectors' gun shop, "Colt on the Trail."
In it, a man told how he shot a nasty bear known locally as, "Old Patch." He used a .45 auto and had to empty the magazine and load four (?) more rounds loose into the chamber to get the job done. He wasn't carrying spare loaded magazines. He presumably used factory FMJ ammo. There wasn't a lot of variety in factory ammo then. I think a .45 auto is marginal.
In the book, a British lady living in India shot a sloth bear with her husband's New Service revolver in .45 Colt. It worked fine. I think she fired more than once, aiming at the base of the white V" mark on the bear's chest. Sloth bears are mean customers and this one caught her as she came down a tree and hadn't recovered her rifle, which I guess was being lowered on a rope from a machan. She was wearing the N.S. and it saved her life.
Another personal account involved a man in Newfoundland with a Colt SAA in (I think) .44-40. He also killed a bear, firing at a distance. I think this was at about 85 yards and was probably ill advised. But he got the bear.
In many of the prior bear threads here, I've told about the Montana game warden who was attacked by a grizzly. It had him down and he opened fire with his service weapon, a S&W M-66 with unknown 158 grain 357 ammo. The sixth shot hit the heart and killed the bear. This was witnessed by an outdoor editor or two and some biologists trying to move the sedated bear. I think it woke too soon, and grabbed the nearest man, the warden. His first five shots were fired in a panic and were not fatal. Then he settled down and shot for a vital organ. Or maybe he just got lucky.
I know of two bears killed with knives. One attacked an angler in midstream. He killed it with his belt knife and a search later found eight human bodies that this bear had stashed in a food cache.
Most PREDATORY bear attacks are by blacks, not by grizzlies. This is not well understood by the public, who think black bears are shy.
Cougars are also a danger and anything that'll kill a bear will kill a cougar.
I have a box of Remington 165 grain .357 ammo meant expressly for hunting. I don't know if they still load it. I have it in case I find myself where I might need to shoot a bear or an alligator. It'd do for cougar, too, but if they were the main worry, I'd be content with Federal's 158 grain Hydra-Shok .357 loads.
A .357 and the ammo are much easier to carry than a .44 Magnum, but if I was really worried about bears, I'd probably use the .44. But that's ONLY if one can shoot one well. I happen to know that I can, but that my recoil and blast limit are reached at the .44 Magnum. If I think I need more, I carry a rifle. Alas, carrying a rifle or shotgun out of hunting season is illegal in some jurisdictions, and can get you in trouble with the game and fish cops. In Newfoundland while fishing, my only weapon was a Randall Model 3 knife with six-inch blade. I was very glad not to have encountered any bears or angry moose. I was only there because that's where the USAF sent me. I wouldn't willingly fish where I couldn't carry a handgun or more. But the RCMP corporal with whom I interfaced in police work warned me that there was no way to legally carry my .45, let alone the .270 or the .303, except during legal hunting seasons. No legal pistol carry at all! (Off base. I did carry on duty and sometimes took my Gold Cup .45 down to a remote area on base and practiced there
. BTW, I fired a few rounds of .270 and .303 into soft earth or mud and the resulting craters were impressive. That's probably what happens inside an animal shot with a rifle. Sobering!)
BTW, I read a true account where two doctors hunting in Alaska were dressing out a caribou or moose when a big grizzly went for them. They'd foolishly set their rifles some distance away and a Ruger Super Blackhawk stainless .44 Magnum was the only gun within reach. It sufficed. I don't recall if the man who wrote up the incident mentioned the exact ammunition.
Go to the zoo and the natural history museum and study bear anatomy. Watch zoo bears as they walk, turn, stand, and maybe scuffle. Think where the vital points would be on that bear if you had to shoot it.