Of course I understand is she's your best friend you'll want to get involved but what I mean is just make sure you're not damaging your own well being through it. I know it is such a difficult thing to deal with because you always feel like you're treading on egg shells but your friend needs help.
I understand if you think your friend can't talk to her parents, since she's 13 i take it your friend is still at school?
Does she have any teachers she can talk to? A guidance teacher, school nurse, any adult she can trust?
Try not to feel so helpless, even by just being there for your friend you are doing something to help her, by the sounds of it you are doing more than anyone else to help her so recognise that you are helping even by just being there.
When you next talk to your friend about this, try not to put a name on it, like don't ask if she is bulimic/anorexic. Instead just as her if she's ok. Explain that you're worried about her and then just ask if she wants to talk about it. If she says no, leave it a couple of days then try approaching it sensitvely again.
Try to get her to talk to someone like a teacher or any adult she can trust, offer your support by saying that if she wants then you will go with her to see the adult she will talk to.
Don't feel hurt if she says she doesn't want you there because one of the things my friend explained to me when she was suffering from anoerxia was that she felt ashamed of herself and one of her biggest fears was everyone knowing how she felt.
Let us know how everything goes.