I don't usually comment but this is such a nice puzzle. In real game play I doubt I'd have spotted it. It's different when you know there is a solution.
I agree with your comment. When I am a piece up, as in this game, I typically go into trade down and win mode rather than even looking for a quick mate. A rook check followed by a rook trade and then win the b-pawn with check is probably what I would do without looking further for something better. If material was even or if black were down material, I would take more time and may have found the mating combination.