My guess is if they only use abx they will be a little leery/out of their comfort zone giving advice on the herbs. You could open it up with a soft touch and ask them if they think it might be a good idea at some point if you introduced Buhner herbs to your protocol. I think they will probably just respond and say let's see how you do with the abx protocols first (which is kind of a stall but I would also understand the logic, try one thing at a time). I wouldn't introduce too much new stuff at once, and if you do introduce herbs I'd try to start with detox and supportive herbs for a while rather than antimicrobial herbs, especially if you are just starting treatment.
I have no idea how touchy your doctor is, I should think most doctors would be chill and open-minded with such a suggestion but then again you never know. Still, if your doctor can't handle such a question then they might not be the right practitioner to help you heal?
I've introduced herbs (including Buhner) in my regimen on my own whilst treating with an allopathic practitioner. I'm not saying I advise others to do that, but it hasn't been a problem for me. I try and research any new thing I'm going to take to gauge how hard it might be on the system and organs. The Buhner herbs have always seemed pretty safe to me, even in conjunction with many abx far as I can tell.