As long as we're considering contributions the bishop can make to a back rank mate, let’s look at another role it can play: it can defend a piece delivering mate against capture by the enemy king.
If you just counted up White’s heavy pieces in the diagram and imagined them trying to mate, you would come up short. He has an impressive-looking battery of two rooks and a queen on the f-file, but Black has two defenders of his own on the back rank; and Black’s king is standing next to the mating square (f8) and so appears able to defend itself by taking the last White attacker to land there. But not really, because the White bishop on c5, while not a threat to do anything on the back rank itself, can protect the last White piece to land on f8 and so provide the finishing touch to a mate. It goes 1. Qf8+, RxQ; 2. RxR+, QxR; 3. RxQ#—because the king can’t recapture. Looking back at the original position, you can see that White had a decisive four-to-three advantage against Black in their contest over f8.