Huh? What? This is confusing to me, Charlie_Harper,

Here's my advice, based on what I understood from your posting - and it's quite simple:

If she is the provider you're thinking she is, then approach her through the ad. Let her screen you as per her normal policy. If it turns out she's not that person, then she should be approached like any other person you'd meet out there. After all, she may turn out to be a provider whose ad you've not seen, but because you've met her in a civilian context, she may wish to maintain your relationship on a civilian level.

I always suggest that women take the lead - for evolution's sake,
the Love Goddess

I'm no Love Goddess, but here is a thought based on something I experienced in this Hobby of ours.

If you are interested in this person in something more than a "pay for play" kind of way, I would NOT approach her through her possible "professional" life.  Why not use the normal, civvy method of asking her out for a drink or coffee, or whatever?  If she says, "No" then you have your answer as to whether she was interested in you or not.  If she says, "Yes" then you have the makings of a possible "real" relationship.

As far as your concept of approaching her as a provider in order to see if you are compatible on a personal/sexual level, I say that is not a good idea for multiple reasons.  First, it may not even be her.  Second, if it is her and you actually have a session, then all you are really going to experience is her "professional" persona.  This is not necessarily her true self.  Finally, if you have a session, she may experience the same feelings one provider expressed directly to me.  That is, "Too bad I didn't meet you in real life instead of this way.  I think we could have really hit it off."

Now, after I heard that, I had a few thoughts.  One, she might have "just been saying that."  Two, she might have meant it as a kind of invitation for more.  Three, she meant exactly what she said and I had "blown" any chance of seeing her outside the Hobby.  Despite having a good time with her, I wasn't especially interested in pursuing anything more so I didn't ask her exactly what she meant.

My belief was that it was most probably the third possibility.  We did seem to hit it off well, but she was very smart and had a successful career outside her providing.  I felt that she didn't mind meeting guys in the Hobby, but couldn't really be serious with a guy that participated.

Your lady friend could be the same way.  Why take the chance?

Just my personal 2 cents.

You have flirtatious behavior with a beautiful woman in a place where women typically do not flirt.  So it is likely she would be receptive to an invite to tea/coffee/protein smoothie in the club cafe or nearby coffee shop. If she likes you there would likely be more meetings and dates in the future.

You have a chance to see if something can develop personally with a beautiful woman where the sex would be real, her response and emotional connection real and not fantasy, and you want to know how to go for the fantasy instead of the real?

That's what's called a rhetorical question.

The others were nice enough to not correct you.

not take yourself, or her, so seriously.

You're thinking too much.  Make a date with the provider, keep an open mind, and if she's the girl at the gym take it from there.

It takes two to tango, Charlie.  Let her have her half of the game.