White To Play And Draw

THE 2019-20 club season began in the Central London League last night.
I turned out on board three for Battersea 2 against Athenaeum.

White to make his 55th move in Stephen Marsland (169) - Spanton (168)

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Believe it or not, and it certainly did not occur to me, White has a draw here, according to my main analysis engines Komodo10 and Stockfish 10.
The game saw a routine finish: 55.Bf1 e5 56.Ke2 f5 57.Kf2 h4 58.Bg2 e4 59.Bh1 e3+ 60.Kg1 Bxh1 0-1
But the engines give 55.h4! as completely equal, eg 55...Kg4 56.Ke3! Kxh4 57.Kf4 Kh3 58.Bd3 h4 59.Be4 Bc8 60.b7 Bxb7 61.Bxb7, and it seems the bishop holds its own against the three black pawns. I can find no way for Black to improve, eg 55...Ke5 is easily met by 56.Be2.
As it happens, a draw would not have saved the match for Athenaeum as Battersea 2 won 3.5 - 1.5.