Well, it's not just about the sex. The way I came out to myself and finally accepted my Bisexuality was when I realized I wanted a long-term, "be with you forever" type relationship with a girl. In my mind, to truly be Bi, you have to want the relationship aspects with both sexes, not just want to have sex with both.
So, for example, if they ever legalize Gay marriage across the country, then those that are Bi can say, "When I find Mr. or Mrs. Right, I'm gonna marry them."
Of course that's not to say that folks can't lean more one way or the other either. That Kinsey scale someone mentioned further back is a good way to address that. And as for the partner "Not being good enough", with Bisexual people it's not that we necessarily want both, it's that neither repulses us. I like sex with a guy and I like it with a girl. Both are different, neither better or worse, and I don't want one more than the other. So if a Bi person is with a guy, they're not gonna be "longing" for a girl cause they're not satisfied and vice versa. More often than not, it's about the person they're with, not the gender.
Hope that helps, having a girl's perspective.