I've seen this type of thread on forums before... I think the general consensus between WG's is... 'Don't approach unless you are welcomed'...
Out of respect for privacy and discretion I would not approach a client in public - eye contact is about where it would end for me.
I know when I am in public, I am 'off-duty' so to speak, and I wouldn't like to be approached by a client... I would expect that if eye contact was made, it would be discontinued if I do not respond in a welcoming manner.
I was on the tube the other night and I may as well have had a sign over my head... Kept seeing a guy looking over and sort of nodding hello... raising eyebrows, constant staring... He moved closer to me and sat almost opposite my seat. This continued and he even said 'seeya' to me when the train came to his stop.
Reviewankly I had no idea who he was, but if he lives close to me chances are he's seen my profile pics etc. It was really very uncomfortable, and he certainly had no encouragement Reviewom me... I found myself staring at the floor in order to avoid his gaze. Not nice.
If it ever happens to you I would go with the 'Pretend I don't know her' stance... We will not be offended!