I'm sure this has been posted before but repetition of something this valuable is worthwhile. Something called AHF, Aids Healthcare Foundation, does free AIDS and STD testing Monday 3-7 pm and Thursday 3-6 pm at Medical City, Building B suite 122.
I went there today and was in and out in one hour. It's first come first served so YMMV. They give you the HIV test result on the spot and take urine, blood and mouth swab for the rest, then notify of the results in a couple of days. They take privacy and confidentiality very seriously, and you can specify how you want to access your results.
I've been paying to get tested every 3 months for about $200 a pop, and Medical City is nearby, so decided to give it a try.
Having been around the Hobby for a number of years, I know that BBFS is not that uncommon. Yes, providers are generally selective and secretive about it--though these days some are quite open in their ads. Just know that if she (or he) does BBFS with you, they surely do it with others. Gonorrea certainly and other STDs can be transmitted through oral sex, so even if you never do BBFS, you are at risk to some degree and should be tested. We owe it to ourselves and each other to get STD testing done regularly.
One hour of your time. No cost. And you get extra horny when your results come back clean.