Do people make fun of her for having an eating disorder? Or are they making fun of her for other things? Do you feel that being bullied is contributing to her eating disorder?
I feel like those are all important questions, along with what do you know about eating disorders? Does she know that you know and has she asked for help? Who else knows about it?
Honestly, I think you can provide support, a safe space, you can try to be there by knowing more about
ED's, etc. so you can know how to support her. But I think it is also important to note that bulimia (and other EDs) are often complex and difficult to overcome. She'll likely need more than just a good friend (e.g. a doctor, a therapist and a nutritionist) in order to help her deal with the physical aspects, such as managing her diet in a healthy way, and her doctor to help with the medical side, such as doing blood work and helping if she's experiencing other side affects like anorrhea (I spelled it wrong but it's where your period stops). Then a therapist matters cause EDs are usually psychologically driven, like were you're being bullied or have controlling parents and focus that lack of control or self-hatred on your food and body.
If I had a friend who had bulimia, I'd do some of the following:
** I'd have an honest talk with her and let her know my concerns -- she's either going to open up or she won't, but at least she'll know I am concerned, that I care, and that I am a safe person for her to speak too
** If we ate food, I'd try to distract her afterwards. I won't post exactly why here because it's triggering and also Google-able but there is a time frame for when you have to purge by vomiting. I might openly let her know that I am doing with something like "out of concern for you, if we're in a situation where food is involved, I am going to try to do what I can to keep your mind off of it so that if you're getting the urge to purge, hopefully keeping your mind off it can help"
** I would also want her input on how I could be a good friend to her -- for example, telling her she can call or text me if she's about to (or has) binged or purged and that we can talk about it, or I would see if there are other things she might think helpful, for example, maybe she'd prefer I take her for a walk around the block if we've gone out for dinner, or maybe she'd really benefit from being able to do things where food isn't involved, and maybe she'd want a friend to go with her to her first therapy appointment and so on.
** if you believe she might have just purged, don't say anything where people can overhear or see, you can simply wait for a private moment and say something like "hey, I thought it seemed like maybe you excused yourself to purge, I'm not trying to call you out, I just want to make sure you're ok". She's not going to get better overnight but having someone who'll check in will help
Also, remember to protect yourself. Having a friend who's experiencing a mental illness like this can be exhausting and taxing on your own mental stability, so don't forget to check in with yourself and take care of yourself; this is also why I believe it's important she gets treatment/care from qualified professionals because you aren't likely to be able to make her bulimia go away and it would be crazy to expect you to be more than a good friend (e.g. you can't be a nutritionist, a therapist and a doctor for her).