How to win this endgame as black?

If white's king moves between those two squares and doesn't move the bishop.

...e2+
Ke1...Kc2
Kf2...Kd1/Kd2
Kxf3...e1->Q+

...right?

Kb2 is possible, I was thinking e2+ before going to Stockfish.

One could relocate the king to f2 and then force the bishop off the board with e2.
But simpler still, I think:

1...Kb2, 2.Ke1 Kc2 3.Kf1 Kd2 4.Bb5 e2+
If white moves the Bishop earlier, b3 falls.

I would move the black king along the 4th rank, around the f3, e3 pawns to reach the second rank (g2, f2 square).
To promote one of those pawns the King must be beside the pawn. An exchange will happen and the other will get promoted.

It's the KP+K theory.

1...e2+ looks winning to me. White can't give up the B for the 2 pawns or he loses his a and b pawns and the game. His only other move that doesn't allow Black to Q next move is 2. Ke1. But then Black has 2...Kc2, 3. Kf2 Kd2 and White is busted.

@Doppel_Adler_6615 e2+ is a great approach, but I don't think it works right away as white can't be put into Zugzwang as he still has the bishop, which he can move in the worst case - but maybe you could manage to put both in some sort of Zugzwang. I like the idea and will check it. Not sure if it works tho. So far we found out that e2 is the way to go and not f2.

@AccurateInaccuracies definitely a good move, but what next? Could you post the full line? How does it win?

@LostEarthworm hey that sounds great! That may be the solution, thank you. So basically you get the king through Triangulation and Zugzwang closer to your pawns and guard e1 for queening. I'll have to check with stockfish.

@Toscani thank your explaining it!

@Mike_in_Virginia thanks!

Thank you all, I now understand the position much better! This sure improved my understanding of the endgame! <3

Update:

I checked with stockfish. You need to play Kc2 and Kd2 to first gain control over d1 (where the king could block the way) while still able to reach the b3 pawn and then e1 to ensure queening, even when the bishop sacrifices.

I know fully understood it and the topic can be considered resolved and closed :)

@xPhilosophusx Part of my reasoning involved your prompt. Specifically, that White would not move his bishop. IF that is true, then the line works (although, according to that same logic, the White king would never move to F2 in the first place, because it is also explicitly stated that the king would only move between E1 and D1). On a practical level, this is a puzzle that was likely drawn from an actual game, so my game theory might not actually apply. Cheers!

@Doppel_Adler_6615 yeah I know you took it a little bit too literally :D Stockfish gave up b3 pretty quick that is why I asked the way I asked. It wasn't meant to be completely impossible, just a thought process. I am not a computer with an IF, I am a human and humans don't think in absolute IFs and IF NOTs. Would have been more clear in a face to face conversation.