So I was playing a bullet game (hence the general mayhem and odd moves) and this was declared a draw through insufficient material. It was a close call whether or not I made my move in time but insufficient material suggests a problem with the software. No?

Just viewed your game.  Black has insufficient material to mate so even though you as white ran out of time its still a draw.  There is no possible way black can ever win this game now.  Hence its a draw. 

Nice thinking blowerd but that would still leave me with the problem of why I have previously won games when I've only had a bishop.

If your opponent had other pieces, they could restrict the king's movement and therefore cause helpmate.

The big kahunas thought that it would be cheap to let someone be able to win with no pieces or pieces that can't give mate so they made it a draw.

Here's a cool helpmate.

This is the game situation in which I won on time with the bishop. I don't think you can have a help mate for this.

Thanks for the info.