Many of the bisexuals I have known (not known in the biblical sense) do not see sexual attraction as either being attracted to men or women, but instead just feel generic sexual attraction towards people, and often without regard to their sex or gender. For them, sexuality is a continuum that they can dive into at whim wherever they wish.

Then there is the political bisexual, which is someone who claims to be bisexual (and may be attracted to people of either gender) but have only had relationships with people of one gender.