We weren't friends for a while because I lost her trust. Our friendship is getting back to where it was before, but I'm afraid of losing her again. That's why I haven't told anyone about this. How can I help?
I can understand how you don't want to jeopardize your close friendship again with this girl. You can be her good friend, but you can't be her parent or her therapist. Perhaps you could encourage her to go to a therapist or school counselor so she can get some advice on how to function healthily in her family. I don't think she'll be very responsive to your trying to convince her to go to a therapist solely for her bulimia. You might also offer to go to a therapist with her for moral support, asking her to go with you so she could learn better ways to cope with her family problems. You might also engage some of your mutual friends to brainstorm ways that she can feel better in her family life. You can ask friends to do this for her without mentioning her bulimia.
It sounds like her family needs to see a therapist so that she and her mom could have a chance at having a healthy relationship. Do you know an adult who's a friend of her mom's who might be able to suggest this idea to her mom? I know that you feel helpless right now in terms of helping out your friend. Try a few of my suggestions and then write back to me with an update. She's very lucky to have you as a friend.