I refrained from commenting here but the Russian guided hunt was mentioned, so I'll chime in. A couple years ago I went to my class reunion (of the later years variety) and one of the "rich kids", now still-well-heeled, was holding forth upon his big bear hunt. I asked him what he bagged it with, .375 H&H or .458 Winchester? He looks me right in the eye and says, why, it was a .308. .308? I'm thinking most guides would put the .375 H&H as the lower limit. Where can you use a .308? Turns out he shot the bear in Russia on the Siberian side. It gets better. He and the guide are out by the camp one night and they spy a bear. Not having his rifle, the guide quickly offers his, after switching on the night vision scope. Night time, relatively small caliber, unfamiliar gun and guide now has no back up. You really want to try a Russian hunt?
Regarding large bear stamina, it was explained to me that, being the largest predator in the Western Hemisphere, these bears have developed an extremely robust neurological system. Consider that they encounter full grown moose and each other. Their bodies have to take a lot of abuse and keep on ticking. My dad had a friend who was stationed in the Aleutian Islands during WWII. One of the guys in his company was always keen to go bear hunting but it was strictly off limits. At a morning muster, the guy is missing. Anyone know where he might be? Well, he was talking about these bears he saw at a nearby stream. They check it out and, sure enough, there is the guy, sort of scattered around the stream bed, his empty M1 Garand nearby. About a hundred yards upstream they find the bear, dead. Fellow told my dad that bear had all eight rounds dead center in the chest. Jacketed ball, sure, but still.....