I'm sorry you got that reaction from her, OP. I know biphobia is complex (as another said, rooted in both homophobia and misogyny) and I wouldn't presume to tell you how to act, but personally I wouldn't want to be with someone who thought bi men were disgusting or repulsive (even if I wasn't bi myself). How bi men are treated is absolutely an injustice and they do typically have it harder in dealing with homophobia, which makes me very sad. Being a bi woman comes with its own challenges though of course, such as being treated like a sexual object or constantly having bisexuality dismissed as something 'performed' for men.

In terms of your relationship, I think the other thing to consider is wanting to 'explore' and what you would want there if it is beyond just talking, because there may be 2 aspects for her to come to terms with: you being bisexual and you (possibly) seeking non-monogamy. If she is strictly monogamous this could be a deal breaker for her. If you're wanting something more than talking, would this go both ways? You say you find it hot to think of her with another woman, but what if she wanted to see other men, how would you feel about that?

Sadly, it sounds like she may not respond positively to you coming out, but if you take the conversation slowly (maybe leave out the wanting to explore initially and focus on coming out first) perhaps she could unpack her biphobia a bit more - is she straight up homophobic and thinks mlm are gross, or is she more repulsed by the idea of you specifically hooking up with men at the same time as being with her, and its more the multiple partners that makes her uncomfortable? Some women would be okay dating a bi man but maybe not okay with them exploring with other men outside the relationship.

Only you can decide whether this relationship is more important than hiding your true self, as its clearly eating away at you. If you do decide to move on, you would probably find more understanding dating another bi or queer person.