I was playing against a friend of mine in my school's chess club today, and that friend happened to have a USCF rating almost 300 points higher than mine (neither of us have very high ratings, mine is 873) but rating was irrelevant since it was a casual game.

I went into the endgame up a pawn and I think I should've had an easy win, but my opponent ended up with a (thankfully) wrong-colored bishop with an h-pawn after I blundered away all my pawns, so the game ended in a draw. I'd like to know if I could've won.

I don't remember the exact position, but it was something like this:

This looks bad for black because white uses the h pawn for bait and plays as in 1...Ba8 2.h4 f5 3.h5 f4 4. h6 Kf6 5. Bd7! followed by Bc8-b7, but I'm not  100%.   

Luke's right. This is a win for white.

I actually played Bxa6. Did that just lead to a quicker draw?

I could see it going to a draw if both sides play right. One bad move from black and white wins.

Well, I also blundered away all my pawns and it ended up like this: