I would just close it without saying anything else. Her communication style online is clearly a very casual one, without any formalities. If you write something like, "Goodbye, was nice talking to you," it could easily come across as insecure and passive-aggressive, since she isn't online anymore. So just avoid that possible miscommunication by just shutting the window.

It would have been polite of her to wrap it up with something like, "Gotta go, peace!" but some people are just very casual communicators online. If she ever just walks away from your mid-conversation when talking in person, that means she is very rude.