thousands of bears are shot every yr with High power rifles and DON"T died RIGHT THERE ON IMPACT!
Yes smaller calibers can kill a bear, no doubt, the name of the game in a BEAR attack, is not to rely on LUCK IMO, but to have more gun in your hand that you can shoot well with,than less!
as stated above, a 22 has killed many bears since its creation, but that doesn;t mean its what you should carry in bear country!,
or certainly NOT what I would be carrying!