"Heterosexual and gay/lesbian people were less willing to date bisexual people than bisexual people were to date them, consistent with anti-bisexual bias rather than mere in-group preference. Preferences against dating bisexual men appeared particularly strong, even among bisexual women."

"Results indicated that heterosexual women rated bisexual men as less sexually and romantically attractive, less desirable to date and have sex with, and less masculine compared to straight men. No such differences were found for heterosexual and gay men’s ratings of female and male profiles, respectively. These results support previous research findings that indicate more negative attitudes toward dating bisexual men than bisexual women."

"These findings extend previous research by demonstrating that negative attitudes toward bisexuals may translate to less willingness to have sex with, date, or be in a relationship with bisexual partners. The differences in willingness between heterosexuals and bisexuals as well as between LGs and bisexuals were stronger for women than men, suggesting that lesbians and heterosexual women may be more concerned than gay and heterosexual men about bisexual partners"

I think this research should to put to rest the idea that men are the ones upholding masculine norms, not women.

If you're a bisexual guy, and you're not looking to date seriously, it's probably best not to tell women about it.