In the business a lady can't be offended by a question like that, no matter how it's posed. However, to be a discrete gentleman, I would suggest you use the reciprocal method.
"I want you to know that I always like to play safely, and that I'm completely clean."
She should be compelled to reciprocate a comment like that with, "I am also clean and like to play safe." or something along those lines. If she doesn't offer a statement like that right away, simply add - "what I mean is, I don't have any viruses or bugs for you to worry about, and I intend to use a condom." If she still does not respond, you now have to simply add, "how 'bout you?" If she's too dense to follow this line, don't back down. You'll just have to ask her straight out.
1) Make sure you make it clear that you intend to play safe and use a condom. Otherwise she may interpret your claims of cleanliness as a negotiation for unprotected action.
2) Remember that a lady who wants your business and money most likely doesn't want you to leave. She will most likely lie about whether or not she has an STD, knowing that she will be using a condom, is in recession from whatever treatment she has had, and will not likely pass it on to you. You will have to be very discerning in how you accept the answer, since the answer will always be no. This makes asking such questions virtually useless.
Questions of any kind will likely make a lady nervous. This is in part why the reciprocal method is the best. You offer information, don’t ask for it. If she seems nervous, it doesn’t always mean she’s lying.
Most importantly, use a condom. Try and get a good look at her before penetration and see if she looks and smells clean. Most STD’s have outward signs when they are in their most viral and transmittable states. Examine her attitude and her surroundings. If she is well groomed and shows outward signs of self-respect, and particularly if her reviews show her to be a safe player, there is really no reason to be worried, in my humble opinion.
A common STD is Papilloma Virus and a woman can be asymtomatic. Its' also something that cna be transmitted by genital contact with out penetration and with a condom on. /The virus can spred from the ladies external genitalia to the man's penis.