Damn, that's a long time to wait for sure but of course she won't accommodate you seeing another girl...lol.
Same thing happened to me today at another place. But I had nothing better to do today, so I waited 25mins past my booked time slot. She made it up by going way over the duration of the session and didn’t even stop when I politely reminded her that the time was up already. They were just super busy.
Maybe you should try and have Anna make it up to you next time. It happens, maybe the previous customer arrived late or the receptionist mixed up the booking. Whatever it was, it sucks to be the one lying face down waiting for 20mins, but I am sure Anna will be extra nice to you next time lol