After our 37...Rxb6 white has to move her queen. She has only 2 squares to move the queen: 38.Qa4 and 38.Qa2.
After 38.Qa4 Qc6! she has two options: 39.Qxc6 and 39.Qa2.
After 39.Qxc6 Rxc6 her attack loses steam (39.Qa2 is certainly playable).
So why not 38.Qa2 instead of 39.Qa2?
So most probably her 38th move will be 38.Qa2
We have to plan our move keeping in mind white's possible h4, Bd5, b4, Rf5 (Bxa5?! is now replied by Qa7!).
Moves to consider are:
38...Qb7. Supports our a-pawn, attacks white's b-pawn. 39.b4 is practically forced. Then we can play Kf8 to remove the Bxf7+-with-check threat.However after 40.Bd5! Qd7 (only good move supporting f-pawn as well as preventing 41.h4), then what? More interesting is white's 40.Kg2! which puts black in almost total zugzwang (only king moves available, both detrimental), e.g.: 40...Qxe4? 41.Bd5!.
38...Kf8?! is the most complicated ine requiring further analysis - does not prevent h4 (next move g5), and leads to complications favoting white - unless some promising variation comes up?
38...Qa7?! supports the a-pawn, but with no other threat (except a5, which is stopped by b5 anyway), does not prevent h4. 38...Qa7 39.h4 Rb7! looked effective, but its refutation is 38...Qa7 39.b4! Kf8 (or move queen, which foils purpose of Qa7)(39...Rb7?! 40.Qa4!) 40.h4 Rb7 41.Qd2!!
38...Qd7 is a sly one - directly prevents h4 (h4? Qxg4+), indirectly protects the a-pawn (Bxa6?! Qa7!) so worth consideration.
38...Qe7?! - appears aimless, doesn't really prevent h4 (38...Qe7 39.h4! Bxh4?? 40.Rxf7 getting our queen).
38...Rb8?! 39.h4 Rf8 saves kingside, but gives away the a-pawn without a fight:38...Rb8 39.h4 Rf8 40.g5 hxg5 41.hxg5 Bxg5 42.Qxa6 giving white a dangerous passed b-pawn plus superior position.
38...Rb7?! This move initially looked playable (Bxa6?! Ra8!)(Qxa6 Rxb2) - is refuted by 39.h4, 40.g5.
Candidate moves for further analysis: Qb7, Kf8, Qd7