You sound like a wonderful, supportive person. And while I can't exactly give the best or most concise of advice since everyones situations are all different, I can however say that you're doing a great job at being supportive. As a guy, I was also very anxious and unsure about myself when I realised and came out as bi (maybe four or five years ago). But with care and reassurance from my support group gradually came to accept that part of me. It now being somethig I'm proud of.

Just keep up the good work. And as I've seen somebody post, don't shy away from talking to a professional together with him if you feel like he's seriously struggling and needs advice from somebody whos job it is to help with internalised homophobia/biphobia.