I have seen my therapist at the grocery store twice. The first time was several years ago when I spied her in the greeting card aisle from afar. I felt anxious and not sure I wanted to say hi (or if she would welcome that), so I avoided her. The second time was in the produce department earlier this year. Our relationship was quite different by then, and I felt/feel a lot closer to her. She saw me but I didn't see her, so she came over and said hi and chatted with me briefly. We talked about it the next time I saw her, and she said she normally wouldn't approach a client in public but that she thought I would welcome it (which she was right about). We were both at the store alone, and I think she had a good enough read on me to predict how I would respond, so it was all good. If it happened again, I would prefer to acknowledge each other. I am fairly open about being in therapy in general, so it wouldn't bother me if people saw us talking.

I don't know if it counts as "in public," but I sometimes see my T in the parking lot/office building corridors outside her private practice. I always say hi and sometimes we chat a bit if we're going the same direction. I would feel super weird if she ignored me there, especially since there are usually few or no other people around.