Can you save white from checkmate? Is white able to recover/win this game after these moves?


And then black takes the bishop:



White resigned after this, what would you do?
First off: I suspect White resigned due to the material disadvantage rather than some immediate mating threat. Having said that, I don't see any reason not to give check on c8 and try to setup some threats here as White, since it seems like Black gets checkmated:

1.Qc8+, Ke7 2.Rb7+, Kf6 3.Qf5+, Kg7 4.Qxf7+, Kh6 5.Qg7#