Because of the nature of the program there will always be a percentage of individuals who cannot "keep a secret". Since it is an "honest program" I don't think it would do any harm in asking this person IF and why she thought it was okay to share your involvement.
AA is not a professional organization. So with that comes the risk of people not following the rules, er suggestions. There is a wide variety of folks who come to AA. Some I wouldn't trust holding a balloon for me. Others I would trust with my life. It comes with the territory. And yes, people do talk. Gossip in AA can be rampant some times. It is sad really. But for the most part, real and genuine people (90+%) do keep it inside the rooms.
I understand why, being a professional and publicly known, it is difficult for some to enter the realm of AA. Yours is one example. I wish you luck going forward. I do know that some travel out of their way to attend meetings. If it is an option, consider it.