Bishop on white remaining, king on black, how to do checkmate?

So I just got into a draw because I only had a bishop on white and he only had a knight, I got into the draw by killing the Knight. The problem though is that his king was always on black, meaning I couldn't put him into check to move him towards a corner, while he could with his knight since the only way to win is to corner them and block their exist with their own piece.

How exactly are you supposed to win in that kind of situation? Unless they willingly gave the win to you I don't see a way out aside from waiting the timer to run out.

If all you have is a king and bishop (and no other pawns or pieces), it is impossible for you to checkmate your opponent.