The adventurous part of me would like to stir up a conversation but given the nature of this business, discretion in public is important.

She could have been headed for a date or coming for a date.

I had this happen to me once, we smiled at each other (I had seen her on the way up) and we shared a nice, quiet ride down to the first floor, and never saw each other again.

what would you have done

I'm leaving an appointment, get in the hotel elevator, and I am joined by a girl who I have never met but I clearly recognize from her backpage ads...  what to do?

If you have a chance encounter like that, you should always act like you don't know the other person; be discrete.

It is an unwritten rule that you do speak to a provider unless she starts the conversation. It is hard enough determining who is L.E. without some stranger talking to her on the street or elevator

I would also ask her if she advertises on BP if the conversation is going well. Too me, it's a great way to do an interview for a lady that I might want to see if I am attracted to her. I would keep the conversation respectful and business-like if I do inquire. To me, it all depends on whether you are attracted to her.

Personally, I would prefer the discreet (proper spelling) smile and being contacted later. as Goddess Jezebel suggests.

if the elevator smelled like that before she got on or was it her that farted.

Geez, this is such simple solution I'm surprised I'm the only one that came up with it!

Maybe I would start singing to myself.

I totally agree. GREAT advice!!!

You should resist the urge to ask her for her fs rate.  Really now, its an unwritten rule that unless you are already engaged as provider/client at the time neither party should initiate conversation or make any gesture or expression as though you are familiar or know the other person.  perhaps a private setting might be an exemption but only if the two of you know each other.  if she does not know who you are, you would make her very very uncomfortable by making any statement which discloses your knowledge of her as a provider.  

I also wouldn't be surprised if she was associated with the provider you had just seen.

Look up at the floor numbers-don't make eye contact-don't talk unless absolutely necessary.
 
Most ladies want to come and go from a hotel discreetly and might feel threatened by someone too chatty.  In fact, many are taught not to get into an elevator with a lone male as it can be a place to be attacked!  And what if it is a case of mistaken identity?  You might out yourself!

It is usually best to say nothing and smile to yourself.  Then post it here on TER.

You recognize her, she does not know you at all.  
I would not say anything to her in that situation.
If I had seen her and we were alone I might politely say hello, but nothing else.
I would not ask why she was there or bring up anything hobby related.  
Her visit may not have been work related.   But whatever her reason for being there, it's none of my business.

How many times have we all seen someone we recognize from somewhere? I just smile and move on with my day.

Devilin

I was out of town once in a motel, checking ads.  Saw one for a great looking lady that was visiting that town.  I really thought about trying to contact her but wasn"t approved and time was short.  So I decided to pass.  I grabbed the ice bucket and headed for the machine.  The door across the hall opened at the same time and guess who came out with an ice bucket.  I about shit.  No doubt it was her.  I had a tough time keeping my mouth shut but did check her ass out as she was getting ice.  Then she came in the breakfast room the next morning and seemed like she was very nice.  Maybe an oppurtunity lost but I did what I"ve always been told to do.

1)  You don't know if she is really alone; she might be on her way to meet someone, etc.
2)  She doesn't know you; acting like that could easily make her suspicious that you are LE or stalking her.

Yes be nice at all times.  But in my case i really wanted to  ""nicely"" say, Hi, how"s tricks?

I tend to agree with this one

What?! Excuse me??!!

I said it's particularly nasty weather, don't you think?