Wow you are so nice! Holy cats, what she was doing is rude.
At the very next cluck during my riding, I'd have said, "Excuse me please," to the BNT during the exercise, stopped my horse, made a quarter turn on the forehand so I'd be facing the audience and specifically the lead offender, stood, stared without a word for 5 full seconds at the offending PITA (observe the squirming, it can be amusing), taken a breath, made a quarter turn back to the rail, say, "Thank you," to the BNT and immediately continue the exercise. The PITA will know the deal, and the BNT will probably understand exactly what happened.
I have no doubt the point would be made. If some slithering coward wants to call me a *itch for mere silence, let them have at it. ;-)
Wow. I was always taught from the beginning that you NEVER interrupt a lesson with any noise, not chatting among spectators (even quietly--maybe in whispers but that would be considered rude too), not even scraping your chair or boots.
Much less a BNT clinician! Wow. Just...wow.
I think there is something to be said for the old-style Euro-military standards of horsemanship...