Depending on the escort, your chances could be higher or lower. I do think it's generally lower if you're going for an intelligent girl who knows what she's doing. Even more so if she's working for an agency.
Escorts don't touch anyone that refuses to wear a condom, so she's unlikely to have a disease in the first place. In many countries, an escort license entails taking the pledge to get tested for STD's regularly. So if she had a disease, she wouldn't be able to continue the business legally.
Moreover, you and the escort will probably be sober when you go to bed. Can you say the same for a girl you meet at a bar? You'll probably be drunk like a frog, and you might do something you wouldn't do in your right mind. You're likely to as well, because she'll look and feel like a "clean" girl since she's not a pro. Just because she charges you beer and martini instead of cold hard cash doesn't mean she's less of a sex machine than a pro, and certainly doesn't mean she's disease-free.
Let's assume you went to a classy escort and she had an STD and still went on seeing guys. Depending on what disease it is, you can still prevent transmission for the most part, also depending on how wild the sex is.
Hepatitis C has a negligible chance of transmission through intercourse with a condom, or any other form of sexual activity involving only one partner's genitalia or other only other body parts of both partners. If you have unprotected anal sex many times with a known HCV+ escort, then there might be a chance, although still close to impossible.
Hepatits B can even be caught by kissing, but there is a vaccination for it. Take all three doses, and then you can inject yourself with HBV+ blood, it won't do you much harm.
As for HIV, if you use a condom, and it's still in good physical shape by the time your "session" ends, that almost always means even if one partner was HIV+, the other is still negative. It's much harder for the guy to get HIV from the girl than vice versa, so even anal sex would be quite safe for you provided there is a good quality condom in use. With oral sex, kissing, rubbing, and such, you have to be really unlucky to get HIV. If both parties have fresh open scars, there is a chance, though still very low. Especially for a man receiving a fellatio.
Genital Herpes transmits much more easily, and that's going to be the biggest of your fears. It's one of the hardest virii to detect, so the girl may have it and be unaware of it. And once you have it, not only you'll have it all your life, it also makes it easier for you to contract other STI's. Using a condom and avoiding "cock-teasing" (rubbing your penis shaft on her vagina) will decrease the chances of transmission big time, but will not exterminate it completely. Funny thing is, a "regular" girl isn't any less likely to have this disease than an escort, since there is no absolute protection, and about 40% of carriers aren't aware of their situation. So in terms of genital herpes, an escort won't be much more dangerous than any other woman. Good news is, even if you have genital herpes, you can keep it in check by medication. It is worth noting that the time of an outbreak or virus shedding make it easier for the virus to jump from one person to another. Unfortunately there is no way to detect a shedding, but an outbreak means having visible cold sores, and no escort could see a client with cold sores on her vagina. So if you don't see any ulcers, sores or pimples on the escort's genitalia, you're *probably* less likely to contract herpes. If she knows she's positive, she could also decrease the likelihood a little further by taking Valtrex everyday she works.
Gonorrhea, syphilis, chlamydia and HPV can also be blocked by a condom quite well. Their likelihood of transmission despite a condom is a little higher than HIV. Unlike herpes, they're easy to detect and treat/cure. With the first three, you're pretty much guaranteed to have it cured if you attempt. HPV, even if not cured, has been known to disappear from your system by itself. And even if it didn't, it's not as dangerous for men as it is for women, even those particularly bad strains. Spraying chemical on the papules to kill the virii and dry the papule is usually good enough for HPV treatment; and in extreme cases, you can usually get rid of the virus completely by having the papules cauterized.
Hope this helps. Merry hunting :-)