My idea here is that white must go Bb2 to prevent black from going b3, followed by Ba3 and b2, but it seems to me that white have two tempos to go there. What forces white to do it right at that moment? Or the idea is completely different?

Rg8?

@Josh Tutin White king is stuck on the H file, black pawn is untouchable and black have all the time they might need to bring the king