As the engine is telling you, after
- .... Bh5
- g4 Bg6
- h4 h5 (basically forced to make space for the bishop; h6 is much worse because white will have the option to open your kingside with g5 and mate you (eventually))
- g5 Ne8 (or Nh7 which is worse)
is a double attack on b7 and d5, which you cannot defend both.
White will simply win a pawn which explains the ca. +1 evaluation.
With 1... Be6 you avoid this whole line.
Not only do you lose a pawn as previous answers told, but there's a strategic idea behind this too. What characterizes the position you gave is that it has opposite-side castles. On this positions, players try to pawn-storm their opponents and break their opponent's king position. With Bh5 you are giving your opponent the chance to start a pawn storm with tempo, which means you are basically allowing him to make his desired moves "for free" and succeeding easily on his plan.