your way was not as efficient as it could have been
Two Bishops Mate Tutorial
what I do is I force the king to the edge mainly using my king. then I force the king with my bishops to the corner my king is closest to. once the king is in the corner I checkmate with my bishops on 2 diagonals next to each other(sometimes you need to do a waiting move)

what I do is I force the king to the edge mainly using my king. then I force the king with my bishops to the corner my king is closest to. once the king is in the corner I checkmate with my bishops on 2 diagonals next to each other(sometimes you need to do a waiting move)
Everyone has a different strategy though.
I hope this helps