She isn't showing genuine concern for your privacy. Friends shouldn't spread gossip around on each other, regardless of who it's to. Those mutual friends are probably further spreading rumors she told them about you.
Make sure you tell her that her behavior hurts you, violates your trust, and you do not want her to share your business gossiping with other friends, no matter what the intent. It's not respectful of your feelings or your privacy. If she's short on things to talk about with other people, she needs to try to be a more interesting conversationalist without resorting to gossip and selling out her best friend.
Do you spread rumors about her? If not, make that point. Also, be careful what sensitive information you share with her from now on. Then, if she repeats the gossiping after you've told her not to do it, then you have a decision on your hands: put up with her gossip or break off the friendship.
Best friends do not behave like this, and if they slip up and tell a secret they apologize.