I have to agree with RichardInTN -- you're still bisexual, but you're also mostly gay. That's probably how I'd try to put it to your dad.
I'm not an expert on coming out, but intuitively I think a short, simple, easy-to-grasp announcement is what you want to shoot for to open the discussion. Don't cushion it with a lot of narration (unless/until your dad asks questions that call for narration); show you're dad that you're willing to trust him with the basic facts (and keep your fingers crossed).
Re: the Bible's support of non-monogamy ... eeg, I'm kind of leery about going down that road. Mainly because it's not your objective to prove to your dad that what you're doing is okay. If you're doing non-monogamy then you obviously must feel that it's okay to do and he can figure that much out. Deciding for himself that he's okay with it is something he needs to do on his own, whether through scriptural study or (what I'd prefer) basic soul-searching.
Now does the Bible support non-monogamy? Sure it does. But it only supports patriarchal polygyny, and women are treated more like glorified property than they are like human beings. I just don't like the Bible as a reference source for how people should relate with each other, even though it does have some uplifting verses here and there (most notably in the Four Gospels). It's gratifying to me (as a polyamorist) to know that something as right-wing as the Bible lacks immunity against non-monogamy, but as a useful tool for coming out to your folks, I don't so much see it that way. I guess you can discuss the Bible if your dad brings it up but try to keep the emphasis away from that topic.
So, what's the best setting for this discussion? Since you don't want to come out to your mom yet, you should only do it at Mom and Dad's house if Mom isn't home. I do think it'd be wise and appropriate to have your wife with you at the time. I'd invite everyone to sit during the discussion.
From there, you'll have to rely on some gut instinct for some things, such as how long the (initial) discussion should be. If you're dad's too shocked to say much, just express your love and appreciation, tell him you'll set up a time to talk with him some more, and wrap up the discussion. If he has a lot of questions and seems calm and reasonable, then a longer discussion would probably be fine.
Other than that it's just general rules of good communication. Don't raise your voice; don't interrupt; don't get defensive; don't try to prove anything; just ask for him to accept or at least think about it. It's worth noting that I think the most important communication skill you can possess is good listening skills. Whatever you have to say to your dad, it's at least equally important that you listen to whatever he needs to tell you. Don't plan your comeback while he's talking. When he's done, repeat back what he said in your own words and ask him if that's what he meant. Seek to understand first, before you seek to be understood. And be compassionate. If he won't be compassionate, at least you can set the example and take the higher road.
Coming out is a tough job. My heart is with you and I salute you for your courage. Also, like the others were saying, your wife rocks too.
Good luck and please tell us how it goes, okay?
With warmth and regards,
Love means never having to say, "Put down that meat cleaver!"