I know Brothels test the ladies often, how do I know if it's safe to daty an escort without offending the lady for asking?

Some ladies will not mind being asked whether they get tested, but some may. There is no way of knowing what the reaction to your question will be so it is better not to ask it. The only way that you will be perfectly safe is if you and the lady get tested and everyone that both of you see get tested and those that they have seen get tested.
My last sentence above seems nonsensical, but it brings up a point that I want to make to you. If you have concerns about DATY, do not do it. The same goes for getting a BBBJ (Bare Back Blow Job). The risk level that you expose yourself to will largely depend upon the choices that you make.
If you do want DATY and/or BBBJs, I suggest that you see only top flight providers because they will accomodate your needs and concerns better than ones that have iffy reputations. Find providers that have shower facilities and plenty of clean towels and soap if you do incall. Always take a quick but good shower before and after. Having a small bottle of strong mouthwash with you is a good idea. Use the mouthwash to throughly rinse out your mouth and throat region after DATY. Also clean your lips and the part of your face around your mouth with the mouthwash. I always do the mouthwash routine before taking the post session shower.

Thank your very much stilltryin25.
You gave me really good info.
I will use it as I go forward in the hobby.
All the best!

sorry, newbie question what is daty?

DATY----Dining at the Y.......eating pussy