Well, MongMan,
Judging from the emoticon and your assessment that "it seems practical to use the place," tells me that perhaps you
a) don't believe your luck
b) don't care for your luck
or
c) are possibly REALLY scared?
Not once in your posting have you stated that you are happy and feeling positive about this turn of events. Everything is "her" and "she." My question is, where are you in this equation? Could it be that you and your ATF are out of sync when it comes to taking that emotional leap, and that she jumped before checking if you also were attached to the lifeline?
Part of the dilemma may be the common belief out there that most guys would be ecstatic if their ATF stopped charging and they became an item. But the truth may reside in something infinitely more akin to real life: for a variety of reasons, some individuals are slower to react, slower to engage emotionally, and slower in becoming emotionally attached to the other party. This has less to do with what she does for a living and more to do with the fact that some women bond a lot quicker and easier than their male counterparts. This is not coming from some sexist opinion about who is better at this or that; it comes from clinical observation and the multitude of relationship-oriented literature out there.
Now, you may just feel that it's gone too fast...or maybe you are wondering if she's even right for you? Again, this has less to do with her profession and more to do with your feelings. Even if she were a waitress/lawyer/librarian/dietician - take your pick of professions - you may not be convinced that she's the one - and again, not for the reason that she's a provider, but for simple reasons of compatibility. The more time you spend with someone, the more you find out whether or not s/he is someone you want to spend even more time with. It doesn't have to be something directly tangible, there can be lots of unspoken things that involve our individual emotions and beings that influence our mate preferences.
Your metaphors about "throwing up," and your question "if there ever really is a point where you just don't think about it at all" indicates to me that you are fearful. In order to think clearly, you will need to get over this fear. As long as this operates in your amygdala, you won't be able to relax and transcend this feeling of confusion and anxiety.
My advice, FWIW, is that if you really want to get to know her and your own tolerance of things in the process is to NOT go to the trick pad, but to meet on very neutral ground. At the same time, you must set some boundaries of comfort for yourself. Do let her know that if this is going to work, she can't talk to you about her business because it makes you uncomfortable. Simple as that. If meeting with her after work "weirds you out," then don't do it. Set dates with her on days that she has not worked and isn't going to work later on. Also, do communicate with her about your feelings. She seems to desire complete transparency, which in your case means disclosing your apprehensions and discomfort. See what she does with it; if she minimizes or rationalizes your feelings away, then that's a red flag for not being heard and not being understood.
None of this has to do with training or being born some particular way. A person's relational matrix comes from both nature and nurture, with childhood experiences and sexual scripting playing equal roles. In addition, your predisposition for handling anxiety, your relational style which has evolved in concert with the maturation of your brain as a child - these factors all have to do with how you handle your emotions and evolve within the context of a relationship.
One last question - she wants to "get a room" - why is it that you can't you meet at her place of residence or yours? I doubt that the relationship will stand a chance if either one of you has emotional issues with hanging out at home. If her profession is part of the reason that you won't even meet at your home, then I doubt that being in a relationship with a professional sex worker is something that you'll be able to handle in the long run.
Walk slowly and forget about the stick,
The Love Goddess