on the outside are mostly in your head. I have done it on many occasions, even when I'm with another lady. As long as you're seeing reasonably experienced providers, and not low-end girls, they are professionals, and other than an occasional glance of recognition, they will not intrude on your private time by initiating direct contact, whether you are alone or with another woman. Hobbyists are more likely to be the ones that commit this breach of etiquette than providers.
I had one instance where I was having dinner OTC with a provider at an upscale restaurant, and a customer she recognized came in with his wife. When the wife went to the restroom, he came over to our table and said to my date, "Aren't you (working name)?" She said yes, but was very uncomfortable. I interrupted, put out my hand and introduced myself as a friend of hers and told him that since he is also a friend of (working name), would he and his date like to join us for dinner? He said no, so I told him that we would probably be finished before him, so we would stop by his table on the way out and chat for a few minutes. When his wife came back from the ladies room, he had the maître 'd move them as far from us as possible, then they hurriedly ate and left before we did. I think it was a learning moment for him. Lol
With that said, I have had a few girls that I knew REALLY well text me when they saw me on the outside IF IT APPEARED I WAS ALONE, and asked if I would like to have a spontaneous lunch or cup of coffee on the spot. I don't mind this. I have never had a girl text me when I was with another woman, my children or grandchildren, or a work associate. They know they shouldn't, so they don't. If you're only seeing classy girls, they will absolutely not make contact if you are with someone else, at least that's been my own experience over the last 10 years that I have been seeing providers. There is nothing wrong when you see her the first time in telling her if she should run into you on the outside to pretend like you don't know each other. They will understand and not be insulted. For most of us, even single guys like me, hobby activities are largely a secret.
If you don't know her well enough to know her real name, do NOT approach her.
That said, when I lived in Dallas I used to see a lot of Asian providers and I also did a lot of shopping at the Asian food markets, since there are only a few of those markets in Dallas I seemed to run into girls I knew all the time, but most of them were girls I knew rather well and partied with on the outside so it really wasn't much different than running into a civvie girl that you know.
I know you have told your dinner date story several times before, but it's a good one and it always makes me chuckle inside. It would have served him right if you did come over and join him. lol