I have bishop he has knight

I was playing a game.  I was left with bishop and king and he was left with king and knight.  It was 3 minutes.  The game did not default to a tie until I took his knight.  My question.  In the case were we both have one piece.  I am left with bishop and he is left with knight is there any possibility to strategically place my king and bishop for a mate?  In other words, does the fact that he still has a remaining knight leave open the possibility of a mate?  Is there such a potential position on the board?  I assumed there was not but the game kept going.  So Ideally if I had not taken his knight, would I have won the game on time?

Yes, if your opponent is extremely negligent and/or *trying* to be mated, I can think of one (and only one) position where your bishop could deliver such a mate:

Sqod there are several positions where you can mate with bishop vs knight.

I only said I could think of only one. If you know of another, please post it.

There are 8 mating positions, but effectively they are one. Same goes for a knight mating against a bishop.

I get it now. You're talking about rotations and reflections of the position I posted: 4 possible corners * 2 possible orientations per corner = 8 positions.

I assume this would be the mate with one knight versus a bishop:

And side with knight can lose on time? Pathetic rules.

much appreciated.  Thanks for the position.