While I don't necessarily dispute Liza's and Kelley's comments upon the inadequacy of the term heterosexual privilege (and in fact I don't think that any discourse on X privilege is very useful at this point in history) and how obsessions with it may have colored the nature of lesbians' views of bisexuals, I think that much of mistrust of and hostility toward bisexuals expressed by a minority of gay men and lesbians are likely to spring from another source: the continuing repression of homosexuality and bigoted attempts to pressure gay men and lesbians into adopting heterosexual identities (or to 'straighten them out').
Throughout the historical periods that Liza and Kelley discuss, and continuing to the present, many gay men and lesbians have had to live with overt attempts by many homophobic parents, churches, and others to 'change,' not to mention the dominant ideology of homophobia. In this context, ideas of sexual choice, fluidity, continuity, etc. that the existence of bisexuals may pose to both gay and straight imagination may be perceived as a kind of threat.
In recent years, some gay scientists have been engaged in a hunt for 'gay genes' and other efforts to identify biological differences between homo an hetero. While I believe that this sort of 'science' is an utterly useless pursuit that is likely to land us on the wrong track politically, it is understandable why some (nay, quite a lot of) gay men and lesbians may be interested in this angle. If gayness is 'scientifically' determined to be 'fixed' biologically, straights may desist in their attempts to change homos into heteros, or so they may hope.
Both a sort of 'biphobia' you guys speak of and gay research in 'gay genes,' I think, are basically a sad testament to how strong homophobia has been and still is and the relative political weakness of those of us who struggle for the end of homophobia.
I'm a bisexual myself, but I don't think that we can expect gay men + lesbians to banish 'biphobia' (or more accurately, 'bi-weariness') as long as fundamentalists can take an ad recommending a 'conversion therapy' in the NYT.
Yoshie
P.S. For a critique of the 'gay science,' consult Jennifer Terry's work.