Now, without being an expert on the topic, perhaps I'm overstepping my bounds...but...
It seems to me that the concept of bisexuality is an attraction to both genders, be it equal or otherwise, but significant enough in both directions that you could end up in a relationship with either one.
According to what you seem to be suggesting, in order for someone to be bi, they would need to maintain two simultaneous relationships, one with a male and one with a female, dedicating equal time and resources of the emotional, physical, and financial nature to both (because, unless I misunderstood, you seem to be suggesting that a) your orientation will change exclusively towards the gender of who you are currently dating and b) you cannot be attracted to anything besides that which you are presently dating)
I'm sure the person still thinks their bi, but no one else does, especially not the person they're dating. Was Anne Heche bi when she was with Ellen Degeneres? Is she bi now that she's married with a child to a man? I suppose, but at the time she was clearly defined as being a lesbian, not bi, and now she's clearly heterosexual. Perhaps by the establishment historical relationships you can say, yes she's certainly bi, but at the time she's attracted to one sex or another, it's not clear. If you happen upon a guy kissing another guy, you don't say, look at those bi people, which they may or may not be, you say, oh they're gay.
You can't define who the person will be attracted to, as they're basing their attraction purely on individuals, so defining them as bi, is just a way of saying they can be either hetero, or gay, depending on who they wish to be with at the time. So it's not wrong to say that Harkness is gay, especially since he had a steady boyfriend though most of the show.
It's really a semantic thing to say, he's bi. It's the difference of siding with the character, and viewing the character externally. As if him being bi, is less of a big deal of him being the main character of a sci-fi spinoff that was originally meant for children. In reality it's worse because bi people have been proven to be the main spreaders of sexual disease among populations.
Him making out with James Marsters was a high factor of being disgusted watching a tv show for me. In my mind because of that he'll always be considered gay. lol