Both times I have said "CBJ please, I think it would be safer for both of us". I can't imagine the provider being upset, especially when I'm vague as to who might have an std.

There is no way that I would risk a BBBJ and then try to explain to the SO how she got gonorrhea.

No problem at all.  You're the one paying for it..., her time, that is.  After all, you're not asking her to do anything extra; in a way, she's doing "less".  Whatever your reason is for preferring a CBJ over a BBBJ (safety, perhaps), there's no reason to feel uncomfortable asking.