If she keeps on bugging you to ride your mare, I would just look her directly in the eye and say something to the effect "Look, she is a very highly trained, powerful, and expensive horse. You don't have the knowledge to ride her and I am afraid you would undo her training. If you'd like, I can help you find a local lesson barn where you can get some riding done on a horse that is more to your level".
I'm pretty particular about the folks I let ride my horses too. Other than family, only 1 other person has ever got to ride my main horse, but he was a stark beginner and was so afraid of screwing up that he did exactly what I told him every step of the way LOL.