Is it possible to win with a king and one bishop vs a king? Are there any possible moves to checkmate a Black opponent if we have a White bishop and king?
No. There is no position you can construct in which the black king is in check (has to be from the bishop), white only has king and bishop and the black king can't move.
The closest you can get is this:
[fen &quot;k7/1BK5/8/8/8/8/8/8 w - - 0 1&quot;]

And the black king can move to a7.