I've seen bisexual friends, whose lives were heteronormative in every way, lose their jobs because they came out as bisexual at work. Just because you've got the opposite sex partner/spouse, the house, the kids and the traditional gender presentation doesn't mean that heteroprivilege can't be pulled out from underneath you at any time like a rug.
Furthermore, there's another name for heteroprivilege and it's called "staying in the closet." Are there lesbians and gay men in the closet? There sure are. And they're staying in the closet, no doubt, to receive the heteroprivileges of keeping your job, not being harassed, and not being subjected to violence. Now those are great privileges and, indeed, everyone should have them but if bisexuals are staying in the closet, it's for the same reasons lesbians and gay men are.
Finally, I can't help noticing that the whole subject of heteroprivilege comes up whenever bisexuality comes up or when a bisexual comes out in a LGBTQ organization. Strange that those same organizations can have heterosexual allies in them and yet the presence of a heterosexual will never provoke the discussion of heteroprivilege--even though they'll receive far more uninterrupted heteroprivilege in their lifetimes than a bisexual/pansexual/queer/fluid person will.
I submit to you that the whole subject of heteroprivilege is only brought up in LGBTQ groups in order to stigmatize and delegitimize bisexuals and dismiss them as valid members of queer struggle. So far, I have only seen it as a tool to silence the bisexuals within a LGBTQ organization.
The author Paige Listeraud is a long-time bi-identified LGBT activist and writer in Chicago's lively bisexual community where she is a member of the Bisexual Queer Alliance Chicago. Coming out at Oberlin College during its Lesbian and Gay Union’s anti-bisexual period, in the bad old days—her active politicization of her bisexual identity has led her to engage in a number of firsts in the history of bisexual activism. She writes bi-furiously on a variety of bisexual/pansexual and queer issues under her nom-de-blog,Max the Communist on her blog at Open Salon called “Living the Bi Life”. In her other life, Listeraud is an actor and also a critic for Chicago Theater Blog.