I ran into the same problem. She goes up those stairs next to where she is found and then exits out the door. Luckily for me I had a recent save that I just started from and made sure I did not let her escape. If you do not have a save to go back to then I am not sure what you can do.
You just have to react faster with her. She will leave. This isn't much different than earlier when you come across that guy being mugged. If you dob't finish the thieves off and run after him, you can't talk to him to get a 50gp reward.