Oh wow, that sounds really awkward! I have not bumped into my T outside of therapy, and although I've read that they wil wait for you to start a convo and judge from your reaction to them, I'd really feel upset and hurt if my T didn't acknowledge me, and I think I probably would have left early too!
Like you my never discloses much in the sense of hobbies etc, although I don't suppose it really bothers me so much And recently she has been dropping some stuff in there which I'm really appreciating.
I suppose you just maybe got to decide if her style suits you still or like you say you want to find a T who is more open!
When are you due to see her next? Can you email/call her and explain beforehand? Or is she maybe likely to contact you?