I thought the definition of 'major' was 'able to FORCE checkmate with only the aid of a King'?
If your standard is 'able to deliver a checkmate if the enemy King cooperates', I believe the Rook also qualifies (can checkmate enemy King near the center of an edge if friendly King has opposition).
But I can't for the life of me think of any reason that would matter. The force mate definition tells you the minimum amount of material you need to preserve to win a simplified endgame. How does knowing that a Bishop could hypothetically deliver a checkmate *if your opponent decides to help you* have any effect on gameplay, let alone piece values?