Now I haven't hunted black bear yet (but I'd REALLY like to), however, I have done a LOT of camping in N. Idaho and seen more than a few.
Black Bears are NOT Grizzlies, a 30-30 should have no problem with a heart/lungs shot, but you would probably need to be within 100 yards. This shouldn't be a problem b/c most of the blackies that I have seen have been pretty close. The dense forests in the Bitterroot or Panhandle should keep most of your shots under 200 yards anyway.
As for a backup gun...the only reason you should need one is if the bear charges you and your rifle jams. I have heard of bowhunters having their partner carry a 12ga loaded with slugs to stop a charging bear.
Hope that helps and good hunting!