It's good that you acknowledge your mistake in walking in like that.
I think Suz has given you a good outline of a "script" for talking about this, and Wild Woman's idea of doing it in the car is a common technique for talking to kids. You don't have to have eye contact but they can't get out of the car either.
Here's where I think you need to examine your own feelings. You say that your daughter is prudish, but you yourself are using terms like "alone time" and "on a place that isn't her back." Why not just say she was masturbating? If this is such a normal activity (and I agree it is), why avoid using the proper vocabulary? I think that sends a huge mixed message that, somehow, there's something not quite polite about this. And you have not had this talk with her, but you're wondering/hoping that she has talking to her friends about it? What makes you think they are any more knowledgeable about it than she is? What makes you think their parents have had the talk you haven't had?
Your daughter is exploring her body and finding what makes her feel good. This is the first step toward having a meaningful sexual relationship in which she will need to guide another person in what makes her feel good. And it's pleasurable and a stress reducer - all good things. She was masturbating in what she erroneously thought was a private setting, but that's not her fault, it was yours.
So, in addition to the talk (and it should be more than one, and you should admit that you are way, way behind and that you have done her a disservice), you can either buy her a book as detailed as the classic "Our Bodies, Ourselves" or you can give her a gift card to buy it herself. I'd suggest the first thing, so it's a gift to her from you and an acknowledgment that we all need help in learning the facts. This book was designed for women who never had anyone teach them all facts, and it teaches the words as well as acknowledges the feelings involved in all of this.
Right now, she's not going to come to you, in part because she is embarrassed, in part because there's been a break in the trust, and in part because she's not sure you're the resource for her. But at least you will leave her with a "Body Bible" she can refer to any time she wants.