I would never approach a client in public, who knows if the wife, girlfriend, children are in the bathroom, buying the tickets, coming with food, etc.  

Proper protocol is that I know you during the moment I am booked... after you leave (or I leave) I have no idea who you are, I don't care.  

Who knows, she probably saw you too and check her phone pretending you were not there. I have done it in the past. I'm always aware of my surroundings, like when Im driving I always check witch car is on the left, rigth, in front what color and type of car... if they follow me or not. Same at the movies, mall, etc. I guess I have PSO's skills.

If she didn't acknowledge you,  then let it be. She smiles, you smile. She comes over to talk....you get it. Unless you are with your wife....then you better GTFO  as quickly as possible!

For some odd reason, airports tend to be the spot I get noticed. However, this is probably because I mostly take the business flights out of/into MSP. Often times, if I see someone I know & they see me, I may give a nod or a smile but that's something I do with everyone I make eye contact with. If I see someone staring at me, I do the same thing and nod or smile. Due to the notion of respect & the need for discretion, I never approach someone publicly & I would hope they do not approach me.

if you can by e-mail or phone to follow up and you can confirm (or deny).
Discretion is of upmost importance in the "hobby."

I take my lead from the provider. Number 1 rule: don't stare.  If she doesn't acknowledge, I don't either. If she says hello, then I do. As a courtesy to her, under no circumstances do I approach her or initiate any type of communication.

It happened to me years ago.  She saw me, smiled and waved. I smiled and waved. She was with a group of people. I didn't approach. We walked away. My friend asked me who that woman was, and I simply said that I knew her from a business meeting years ago.

It's not really a big deal.

First time I spotted an escort in public, that I had seen a couple times, was when I was leaving an appt at a local hotel.  As I crossed the parking lot, I saw her, smiled and thought just keep walking. She was in her car smoking a cigarette and texting. When we made eye contact, she waved me over and rolled down her window. She asked how I had been. I said that I was going to contact her soon about another appt. Then she asked who I had just been with at her hotel. I lied and said I had just dropped off a co-worker who had an early flight the next morning. I made another appt with her a couple weeks later, and was glad I had seen her in the parking lot.  

Round two. I was at local event where lots of people show up and there are vendors selling all kinds of things from food to jewelry and trinkets. I was there by myself, looking at the stuff for sale, when I spotted someone I knew from 5 years ago that had left the business also. I had sex with her many many time over a 5 year period. When knew each others back stories. But when she quit, we stopped communicating and I moved onto other favorites. I maneuvered myself in the crowd, so that we could make eye contact, just like happened in the above scenario. She did not respond, and pretended to not notice me. I kept my distance. Then this guy comes up to her and hands her some food and drink. I backed off, and was glad that I had not forced my attentions on her. I am sure she would have handled it the same if she had seen me with another woman. Thanks to all the ladies out there that practice discretion. You never know how close someones significant other could be, and how that could ruin that persons life.

... just smile as you to any attractive woman and walk in by. make it clear you have no interest in stopping and she will take the cue generally. Easy.

... guys contact me later on saying they saw me somewhere which is cool and how it should be done.  
Only once did I bump into a client in public (like we literally almost bumped into each other) but we smirked at each other like as if we were any other random strangers said 'excuse me' to each other and kept it moving. I'm rarely out and about alone.  
I don't know who is with you or near you (and you don't know whose with me).