I don't, no -- only to two very close friends, one of whom has been hospitalised for anorexia because her organs were closing down on more than one occasion., the other a therapist I'd asked for a recommendation for a specific form of therapy locally. And when I say 'talk', I mean, I told them about it once, years ago.
I have many other friends I love and value, to whom I've never mentioned it. It's a very vulnerable thing to do. I'm not 'withholding' crucial information from them, I'm simply not able or willing to be vulnerable about something very difficult and personal. My disordered eating started when I experienced CSA as a child, and that's not something I talk about easily either.
Obviously, as a PP said, you can discontinue a friendship for any reason. But to require someone to tell you about a complicated disorder which is bound up with so much shame and self-loathing as a condition of friendship strikes me as unreasonable and cruel.
In your shoes, I'd be asking myself why it's so important to you that she discloses her disordered eating to you. (Unless she's visibly extremely emaciated to the point where you worry for her on medical grounds, in which case I do understand why this is difficult to witness. But it's difficult to witness when you know about the anorexia, too.)