What you described is more akin to panloveuality. Some biloveuals have a preference. I'm not biloveual, so I can't say whether this is for physicals reason or psychological, however.
My good friend Night Fox is an example of someone who's biloveual, but has a strong preference to men. Given the fact that he's homoromantic, I would guess it's psychological, but I've never asked, so I'm not sure.