White has the advantage due to the extra pawn. White’s king is also close to the pawn. White’s goal is win, which will require queening the pawn.
Black’s goal is to draw. Black can draw if his king can reach f6 or f8 since white will not be able to force the king from the square, or if he can capture the pawn, even if it results in the loss of the bishop king white will not be able to mate with a bishop.
Move 1 by White
1. f5 draws after 1. f5 Bc2 2. Kg7 Bxf5.
White has five king moves. Ke5, Kf5, Kg5, and Kg6 allow black’s king to easily reach f8.
Kf7 has a number of drawbacks. First, it blocks the path of the pawn. Secondly, it reduces the mobility of white’s bishop. Thirdly, it increase black’s dynamic potential by allowing a check on the e8-h5 diagonal and potentially on the a2-g8 diagonal.
We therefore have identified one candidate move thus far – Kg7.
White has eleven bishop moves…
Bc8, Bc7, Bb3, and Bg4 lose material without compensation.
1. Bc4 also always black to easily draw after 1. … Ke8 2. Kg7 Bg4 and white cannot advance the pawn without either losing the pawn or allowing Kf8. The same applies to Ba2, Bd5, and Bg8.
1. Bf5 Ke8 2. Kg7 Ke7 and now white’s king cannot move since black can draw with either Kf8 or Kf6. And now 3. Bh3 Bc2 4. Bg4 Bd3 5. Bh5 Bf5 6. Bg6 Bg4 and white cannot make further progress.
This leaves two moves – Bf7 and Bh3.