You haven't provided enough information for a qualified answer. We don't know about the relationship of the guy who is the father, with the woman who is bearing his child. Is it blossoming? Is he in love with her? Is he in love with you? We don't know much about your relationship with him.
Unless you like sharing, no matter what the nature of the relationship of the bi guy, it's a regular can of worms. Perhaps you should have thought about it before going down the path of dating someone bi.
If he's truly bi, he might marry the girl, and raise the child in a conventional nuclear family, that might well be happy. He might set his "bi" nature aside for the sake of the child.
The test should be is he in love with you? Are you in love with him? If the answer is no, it's probably best to be selfless and to allow him the opportunity to see where his heart lies without outside interference. I think you're headed down the right path there.
Another test should be are you prepared to accept a bisexual man, with a child, and with another lover (his girlfriend, other women, or other guys) into your life? Are you prepared to share him with others? If the answer is no, you need to move on.
You should also ask yourself where else his unprotected dick has been. Is he the responsible sort? Doesn't sound like it does it? Are you prepared for whatever else he might bring home? Do you think he's a monogamous sort, or is he more of a swinger / bi?
What's right is to do the selfless thing. Ask yourself what that is. If the answer is allowing him to sort it out with his girlfriend, and to allow him to decide what to do about parenting his child, the the right would be for you to step aside / move on for the time being. Remember, it's not always about you.
No matter what the case, he likely should be given some space, and time, to decide his relationship with the mother of his child, and how he's going to deal with it.
Ever study battered-wife syndrome? Ever study fatal attraction? I think you know what you should do, but, are seeking approval. Do what's the right thing, morally, for all of you.
In a world of 7 BILLION folks, it's kind of weird, sometimes, how we set ourselves up for grief that we probably would do well to do without. I suppose it's a human trait, as many folks don't think clearly and logically. You have to look deep inside and ask yourself if you're up for sharing this guy with many others. You have to look deep inside and ask yourself if you should (if it's plausible) give the child a chance at a conventional family. If the guy is gay, and just not admitting it, that's a whole 'nuther thing, but, no matter what, it's a high drama, high steaks, game where someone is gonna' get hurt, and it's most likely gonna' be you.