Actually, after 1...Kf5 2. Kd4 Kf4 3. Kd3 h3 4. Ke2 Kg3 5. Kf1, 5...Kh2 is a huge blunder, allowing 6. Bd7 with a draw. The right idea is 5...h2! sealing the K off from g1 with the pawn and forcing the B to stay on the long diagonal. Then the other two black pawns advance to g4 and f3 and it's all over.

I don't know if there is a shorter win here or not, but I would just play 1....Kf5 here without thinking about it. I would think the main danger in not winning this is white's king reaching the corner and white giving up the bishop for two of the pawns to reach a drawn ending with black still up a pawn. So, I would play 1.....Kf5 and 2.....Kf4 as the first two moves so that the king can't be cut off from reaching h2- from there black can confortably advance the g and h-pawns to h3 and g2 escorted by the king.