Can A King Alone Win?

Last night I played with Buck (2400+), a fictitious player in Chessmaster GM Edition, in a 10 minute rated game (I have been using the software for almost a week now).

In the endgame I have one h-pawn plus a light squared bishop (I played White) against his King alone. It was so silly that I tried hard to promote the pawn and didn't know if a wrong bishop cannot help a rook pawn. But I'm not 100% sure if a wrong bishop cannot win the game? How about a knight?

But the thing that surprised me was when I tried to move my king around the corner to find a way to promote the pawn, I lost on time! Is it true that a king alone can win on time? I thought it should be insufficient material? 

Wrong bishop color, it's a draw.

A knight+h pawn vs. a king is a win.

Of course, you can't lose on time vs a bare king, that's a draw.

Thanks Natalia! Looks like now is the time for me to upgrade my endgame skill (has been on the list for a month or two). I'm happy that my endgame skill is starting to become the weakest link now after I work out my tactical skill :))

So, it was Chessmaster mistake. Hmmm. Quite unfortunate knowing that I really like that fictitious personality feature.

Edit:  This post is about B (light bishop) + P (h-pawn) + K vs K.

You can only win if you can keep your opponents king from reaching the h8 square.  If your opponents king can reach the h8 promoting square safely to block the h-pawn then you will only get a draw because he will just shuffle his king between the h8, g8, and g7 squares (staying within 1 square of h8).  You might like this sequence of moves:

Oh my god! May be I had the chance for that kind of maneuver in the game! Thanks einstein_69101.