Would like client as well as provider perspectives on this one.  

If I see a provider I know fairly well out and about in the city we both frequent as our home turf, do I say hi if it looks like we're both alone?  Or is it best to just avoid outside contact altogether?    

I obviously don't want to be rude to her, especially if she's a regular. But, I guess you never know who might be with each other, or if she's OTC in real life or not. Same goes in the opposite direction. Should the lady avoid making contact with me at all costs, even if it's clear I'm on my own

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Of course, all good tips. I was thinking more of the subtle hints, not the obvious overt actions was what I'd look for or give off myself.  Thanks

as she is picking out cereal, "Mmm, I love Captain Crunch too."

HAHAH, but yeah. Julia is right on all points. I've told gentlemen that live near where I live it's OK to stop and say hello if I'm alone though.

a very subtle nod and a smile works perfectly. The problem with dropping subtle hints is you don't know if she's on the same page as you are in that realm, and it could lead to an awkward encounter if either one of you misreads something.  

Nod & smile

...a smile and a nod of the head are considered standard protocol when passing someone on the street. In NYC, you shouldn't be looking at anyone anyway, so shame on you. In Chicago or Detroit, a kevlar-to-kevlar chest bump is appropriate. And in Colorado, offering her part of your brownie is considered the cool thing to do.

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Agree, a nod of the head as you would an amiable stranger as you pass.  One can not be certain of the other person's friends & companions who might witness & question.  You can have a laugh over it at your next 'in private' meeting.  There might be exceptions but this is the safer course.  It is better to be prepared than to stand there looking odd & draw attention...  causing a scene you were trying to avoid.