Hold the draw for 16 moves · You play black
ProA bishop and a rook pawn are a whole piece and a pawn up, yet it is a draw when the bishop cannot control the queening square and the defending king reaches the corner. The race to the corner is the whole defence.
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White has a bishop and a pawn more, and it is still a draw if you know where to run. The pawn is on h5, the white king on e5, the bishop on e2; your lone king stands on e7 and it is your move. Sixteen moves to hold.
A rook pawn queens in the corner, here on h8. That square is dark, and the bishop on e2 only ever stands on light squares, so it can never take h8 away from your king. Get your king into the corner and White can do nothing with it: on h8 the king can never be checked, and boxing it in only gives stalemate. The extra piece is worth nothing.
So the whole defence is a race, and from e7 two moves win it: Kf7 and Kf8. Both head for g8 and h8 at once. Every other move is a tempo short: from e8, d7 or d8, either the pawn runs or the white king steps to f6 and shuts your king out of the corner, and then White queens.
Once you are there, move between h8, g8 and h7, whichever squares the pawn leaves you. White can push the pawn and bring the king up, but the best it gets is stalemate. Swap the bishop for a dark-squared one and the same position is lost, because then the bishop takes h8 away and the king is driven out.
Play Black. Your first move is the one to think about: count how many moves your king needs to reach h8 and how many the white king needs to reach f7 or g7. After that, stay in the corner and do not come out to chase the bishop. Sixteen moves with the pawn unpromoted is the draw, and stalemate counts too.
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