It's customary not to acknowledge such public encounters in case one or both persons is not alone or in some other way might not welcome contact. Even if both parties are alone, contact may not be welcome.
I'm guessing you were alone as well. Under those circumstances I highly doubt it would have caused a problem if you had acknowledge her presence but there was certainly nothing wrong with not doing so.
This happened to me at Target. She was parked next to me. She was getting out of her car as I was about to get in mine. We made eye contact and each acknowledged the other with a slight smile just as I might with any pretty girl. That was it, we both went our own ways.
Several years ago I saw a provider that I was seeing regularly in a bar. Thinking the right thing to do was nothing, I didn't acknowledge her. The next time I saw her she started teasing me saying "so you think you are too good to talk to me."
I explained that I was just trying to be discrete. She said if I saw her again in public it would be ok to talk to her. Never did see her outside of a session again.
A few years back someone posted here that he saw a woman jogging around a Minneapolis lake with her P number printed on her t-shirt. I thought that was pretty brilliant marketing (for those in the know.) Actually anyone looking it up in a google search would figure it out.
If your both alone and she initiated why not
A few years ago i got into line at Cossetas there was a girl and her mom in front of me. I looked at the mom and was admiring her figure from behind. Then she turned around and we both recognized each other as she was a regular who i would see while she was utr before she decided to give up the life, we just kinda of smiled at each other and went on our way. About a month later i got a call from and she wanted to get together, so she came over that night. We talked had a drink and puffed one for quit awhile about life, we hadnt seen each other 3 or 4 years. Then went upstairs and had the most sensual, loving and fulfilling 2 hours or so time of our lives no clock involved. Anyway she calls and stpos by once in awhile.
The hobby is a circle, don't mix circles is what I say. Meaning, don't let people in hobby into your other life circles, home, work etc... Its a rule that has proven to work for me. My .02
I see one of ATFs like twice a week in the gym, we always say hi to each other. I have seen a couple of providers in social settings, just read the room!
I would say it's polite to at least acknowledge her...unless you happen to be with a significant other or someone else who shouldn't know about your secret connections. As long as she's being discreet, I don't see any problem with a little flirtation, or even casual conversation.
I've worked at many a company, so if I ever met a provider (hasn't happened yet) in public with wife or family around me, I would have no problem acknowledging her and even chatting with her. I'd just say it was someone I used to work with ... without explaining our workplace roles. 
This has happened several times. My policy is to mom I wave them alone unless they initiate contact. One time I was at Regions Hospital visiting my father in-law with my wife. One of the nurses was someone I was familiar with. She smiled from a distance and in a way that would not get me in trouble. I saw her a couple weeks later and she said she appreciated that I didn’t try talking to her.
I saw a provider at the grocery store a few weeks ago. We were both wearing masks. I recognized her, but not sure if she recognized me.
She was with another female and I heard her talking and knew it was her.
Didn’t speak with her or anything. Just let her do her thing.
Many moons ago I had a late night encounter with a lovely lass at Relax a lounge upstairs. We talked somewhat before my leaving. About 6:00 in the morning went to a nice breakfast stop. And she was my waitress. We both couldn’t stop smiling. Gave her a big tip. Both times.
Several years ago, my wife and I were leaving a restaurant, and my ATF was also leaving with a group of women. We saw, but didn't acknowledge each other. Later, the provider told me the encounter made her uncomfortable -- the reality poking in on the fantasy. To each his/her own, but as a general rule, I say don't acknowledge a provider you see in public unless she makes the first move.
The only time I saw a provider in public I was leaving another lady in the same complex. They knew each other and did doubles. Well the first lady walked right up to me and said "I know where you have been and what you were doing with who". Well after I said hello we realized we weren't supposed to know each other. We then had a good laugh about our reaction to seeing each other.
About 4 years ago as I was leaving a once upon a time regular who isn't on here anymore (but still active), I ran into 2 other providers downstairs going to see her. As the story goes she forgot she had friends coming over and had to cut our date short. She offered the "half off next time" special which she did to me a few times that year. Well we hung out and talked until she had to buzz them up. We passed each other in the hallway but they had no clue who I was. It was winter so they were bundled up but seeing them verified they were definitely not my type. One is still around and one moved to Denver (I think) a few years back. They had that alternative look to them that I never got into. So she pretty much saved me lots of money that night.
