It would be nice to see a diagram. Was it like this:
bishop check mate

No, almost all the pieces were on the board. I had probably only made three moves. The bishop was right next to my king. The king couldn't move anywhere else because all the spaces were occupied, but it seems to me that he could have taken the bishop.

If the bishop was protected, you can't take it.
It's an automated system that checks for mate so...
Only 3 moves? From the beginning? Here's one example of a mate in 4:
I just played my first game of chess here on the computer. The computer said that game was over and that I had lost even though it looked to me like I had a way out of check. There was only one place my king could go, and that would be to take the bishop that checking me, but the computer said the game was over, so I'm wondering if there is a rule here that I just didn't know. Can't I take a bishop with a king on the diagonal?