I'm not suggesting infidelity. What should a person in this situation do?
Well, Front-Ranger's answer is both better informed and more eloquent. But my answer would be, whatever the person should do isn't necessarily any different than what a straight or gay person should do.
Again, as I understand it -- and people with firsthand knowledge can correct me if I'm wrong -- the fact that you're attracted to people of both sexes doesn't mean you
need to be with people of both sexes. It just expands your options. That is, if you're a bisexual man married to a woman who is no longer interested in sex, you can have an affair with a man or a woman (assuming you can deal with the moral implications of the infidelity). Or you can get a divorce and get involved with a man or a woman (assuming you find the divorce part morally acceptable). Or you can get your wife to change her mind. Or you can not have sex.
In other words, you have the exact same options as you'd have if you were straight or gay, only your other partners could include people of either sex.
The way I understand bisexuality, as a straight woman, is this: Let's say I'm attracted to both George Clooney and Brad Pitt. That doesn't mean I must have sex with both, it simply means I'd be happy having sex with either. If I were bisexual, I might feel the same way about George Clooney and Angelina Jolie. Same thing -- I don't need both, but either one or the other would do.
Again, those of you who know from firsthand experience can correct me if I'm wrong.
I used to think that bisexuality offered the best of both worlds, as presumably it put the entire human race up for grabs, so to speak, as opposed to just half of it. A bisexual friend educated me that it's a bit more complicated than that -- that there are social challenges, the neither-fish-nor-fowl identity that Front-Ranger alluded to. So it's not easy street. But maybe someday, as social attitudes lighten up, it will be the ideal.