I have hunted with several Bear hunting guides, All carried 12 Ga shotguns for back-up. Thats good enough for me.
That's fine if you don't have your hands already carrying something or hunting Elk in Grizzly country. If you'd happen to get into a tight spot in a situation where you can't be carrying a shotgun besides a rifle, I'd still carry at least a .44 mag at my side. At close range anyway a scoped big game rifle can be tough to make any kind of accurate shot with.