A key thing here... did she ask you if you minded staying?

You mentioned the transit stop being 20min away. I assume this is a walk which I figure is a ten minute drive. In my book this is not out of the way. If it was a 20min drive (40min round trip) then I see that this does make a difference. What was wrong with her mother that she could not have driven you to the stop by the way? I certainly would have. Was there someone you could have called to come help you? Again, I would have.

Incidentally, I can call mobile crisis here and they will give me a ride.