Great point!
One bishop and king vs king and enemy bishop
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Which computer umpire? They all do something different but none of them do it actually according to the chess laws because it may be hard to calculate.
I think chess.com's umpire gives you a draw due to "insufficient material" though no such law exists officially.
Note: K+B can only checkmate against K+B when the bishops are of different square colour - and both sides cooperate to get there.
Everyone knows it's stone set impossible to win a king with just one bishop along with fellow surviving king however if all you have left is a bishop and king and your opponent also has a bishop and king remaining (thus 4 pieces left on the board in total), the computer umpire does not automatically call it a draw - it's still play on. Does this mean it is possible for one bishop and king to mate a king without a second bishop or knight if the enemy king has a fellow teammate remaining, in particular a bishop or pawn?