What does “by request only” mean??  Are they fishing for interest from a city?  Or looking for “fly me to you” requests?

Thanks in advance!

Still thirsty

My guess is that you'd have to ask a provider in person for any special requests you have.  

When I post by request only (witch I do often)... is bc I am not sitting in a hotel waiting for a call.  
I go pretty much anywhere between Richmond VA to Baltimore MD (DMV) DC-MD-VA on a weekly basis due to my civvie job... so I can extended my "lunch" anywhere or adjust where I am for "dates" and civvie meetings... Gotta love have a job that allowed me to adjust my schedule as I need it.

I should have added this is in my hometown visiting lady section.  She homebases three states away!
Put in her visiting ad no dates, but rather “ by request only”
Thanks again

I will come to your city if you request me to.  It may be a minimum of time booked, depending on where you are.  My fly me to you package means I'll fly anywhere in the US for an overnight.  
XOXO  
TL

ie relative easy. Sometimes in the  morning I can be in Richmond VA.. and in the evening in BWI... (I already in one day drove VA-MD and I am relatively close to DC).

You could just post a link to the ad, and I don't think that this is the case, but some include "By PRIOR request" or "By PRIOR arrangement" only if it something out of the ordinary or needs special preparation. E.g., if you are hoping for anal, some need to know in advance. Special outfits or instruments (of pleasure or torture) she might have to pack in her bag sometimes needs prior notice.  
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What others have inferred, "I am only in your area by request only," seems reasonable in your case.  Depending on the location, she might also ask for a deposit to certify the request.

"by request only"

If I get a min request in New York-Chicago-Boston Raleigh (with min 3 hrs booking) and the client take care of airfare.... I have done it few times.  

Leave early in the morning... have a great day... come back home late at nite.