STD from a nude massage? Seems unlikey,don't you think?

Simply tell her to leave them on. You can say that you like to see a woman in her underwear.
Elvis Presley was notorious for having girls run around in their underwear. In fact, I like it too.  

I do think you are over reacting about STD's. You are getting a massage. You should worry more about her hands being clean then an STD.

You're just getting a massage and hand job, but you're worried that you'll catch a STD if she's standing there without panties? It doesn't work that way, of course, but I'm sure she'd be happy to keep her panties on. But if you're that paranoid, you should consider if seeing providers is the right choice for you.

Dear Chris:
I ask yourself this question first? How do STD's emanate and what is the culture that bacteria grows into a disease? Then follow up with the question of how bacteria lives?  Then ask yourself a third question of how many parts per billion would she need to transfer before the disease is active and detrimental to customers? Once you ask yourself those questions and get the correct answers then you will be more well educated on STD and how they fester and what the dangerous levels are. Also go on the CDC's website and do a search about how STD's are transferred.

You should act within your comfort level.  If that includes her leaving her underwear on then so be it, you are the customer and I suspect that she will happily oblige.
As suggested above, just tell her that you find it sexy.  Do NOT tell her it is because you don't want her to give you an STD, LOL.

Yes, definitely refrain from mentioning STD's during the appointment.  I would also suggest complimenting her on her lingerie when you walk in the door, like "I love your outfit, it is so sexy, will you please keep it on for me?"  That way, you both won't feel awkward when she's about it take it off and you get all freaked out and nervous and shout "NO, keep them on!"

But like the others, I think you may want to consider how comfortable you are with a FBSM, period.  You don't want to be flinching during your body slide because you're thinking about what STD you could be getting - you should be enjoying it, loving it, and wanting it.  

Getting an STD from a FBSM is very unlikely and most providers will be squeaky clean for each appointment, freshly showered.  And they expect you to be clean as well.  Most also offer a shower for you at the end of the appointment.