[Eternal]

Honestly most people with disorders have this problem, I've gone through the same thing. It's hard to talk about it because you're afraid of those you love getting in your way and preventing you from whatever destructive behaviors your engaging in. You know your eating disorder is bad, but you're afraid your boyfriend will be upset and make you guilty, or take an active role and this would then mean you can't make your own decisions as to whether you stop engaging in them or not. That lack of freedom is what makes it scary to speak out.
That being said, I still think you should talk to him about it. He's your boyfriend, he loves you and should be there for you. If you keep this to yourself, it will make it harder to recover and begin eating normally.
If you're too afraid to tell him in person, send a text, write a letter, or send an email. It doesn't necessarily matter how you tell him, just that you tell him. Those are all non-confrontation ways as as long as you can get yourself to press send, it's easier to do than face-to-face contact.
Once it's out there, you can try and take control and tell him how he can help. That way you can hopefully prevent him from being too intrusive, or from just being disappointed. People often don't know how to help those they love with situations like these, so figure out how you would like him to react and act, and be sure to let him know.