It was a bad date. I wouldn’t sweat it so much. Not every connection goes places.
The “right” way to handle that situation would have been to sit down with them and just chat. Being an introvert though, if I were in that situation, I would have just said hey, then politely said goodbye, headed home, and gotten feedback later about how she perceived the date. It was a bit rude to just leave without saying goodbye.
I wouldn’t make too much out of the fact that she was talking to another guy.