It may be that she is a little distant because she's not sure what you would prefer.
I often see my clients out and about. I never say hello or acknowledge them first - if they say hi to me of course I'll say hi back but I never initiate contact.
I do it because I don't know if they want anyone to know they may have seen me. It's probably a little different with your gp but I'm always really aware that people may not want to explain why they know a lawyer (especially a divorce lawyer).
I don't meant to be rude at all - I just don't want to make any of my clients (including previous clients) uncomfortable or having to explain to someone.
Just another perspective