What kind of bears are you likely to encounter, if blacks, big penetration is not hard to come by, bones are not that heavy. In a true life or death head on encounrer, SSG might be better. Just keep pumping away at the bear's head. While you will likely kill it with the first shot, blowing away the eyes, ears, and nose will make it awful hard for the bear to find you.
A lady I know ran into a bear while bird hunting with her boyfriend. She was terrified of the idea of being eaten by a bear, so he had instructed her to empty her 12 ga at the bear's head if the situation arose. He got her to load her pump with two #6's, followed by an SSG. When the inevitable close encounter happened at a distance of about 15 feet, she stopped shooting after the first two shots as there was no more head to shoot at. The bear was a medium sized boar.
The lady also happens to be a championship class trap shooter, so the patterns were nicely centred!