Bisexuality =/= flirting with everyone you meet.
I am LGBT, and I don't care about LGBT representation in Civ. It would be cool if it was there, but not at the expense of having interesting leaders. I had no idea Hadrian was gay, and it doesn't matter to me that he was. But for people who do like to associate with the character they are playing as, it may help. I care a lot about that in games when I actually get to see my character and act as them, but Civ is not one of those games.
As for representing sexuality in Civ at all, I think it should only be used where appropriate. For example, Theodora and Catherine in Civ5 were very sensual because the real people were. But just because someone is bisexual doesn't mean that they flirt with everyone, and in fact there may be no good way of showing that they're bisexual. If their sexuality is not an important part of how they interact with others, why would you go out of your way to misrepresent them in that way?
If they were famous for acting sexually, then represent them that way. Otherwise, their sexuality is not relevant to Civ diplomacy. Put it in the Civilopedia, though!