What rifle round would you recommend to kill a bear?

The .308 or .30-06 would be fine for hunting. I would want a .454 Casul handgun at a minimum or if you think that you can get by with a rifle for self defense from a bear, I would go with a minimum of one of the .338s or the .375 H & H Mag. There is quite a bit of time for a bear to die while hunting, but you need to stop them very quickly if they are attacking.