As a straight male (well, mostly - I follow the 'If its pretty, f*ck it' school of sexuality, and only females have fit the bill thus far), no, I have no issues with being in a relationship with a bisexual woman. In fact, that's about the only context - in a relationship w/ a bisexual female that I really like - in which I'd be comfortable with a 3-way as anything other than debauchery without a shred of love/romance.
On the flip side, I personally find gay male sex to be gross - I don't have any moral quandaries with it, I support gay marriage and similar issues, I've had gay male friends and relatives, but I find the act itself rather disgusting.
Like pooping, or childbirth. Or, a combination of the two, really.
As Dave Chappelle once put it: "Sorry, I just find it to be gross."
That said, if I were theoretically a woman?
Well, theoretically, I'd probably not be too keen on dating a bi-sexual guy, just like I wouldn't be too keen on dating someone who was into any of a wide variety of sexual preferences/fetishes that I don't share - if that's your thing, cool, more power to ya!... but it would not be my thing, and it would likely really turn me off to know you have/will/would like to engage in that kind of sexual activity (namely, in this case, male-on-male sex); doubly so if I felt as though I was holding you back from exploring such scenarios.
Of course, that's all theoretical, but I make that judgement based on the fact that, non-theoretically as my straight-white-male self, I've avoided relationships with women because they were into things I distinctly was not and could not be into - and knowledge of that interest was a turn-off in its own right.
To be honest, I feel as though there is no right/wrong answer on something like this - its entirely up to the individual, and how they perceive things, and making the decision one way or the other can be driven by any of a variety of motivations.