This is a complex question, but I have a few minutes, so what the hell:
First and foremost, yes, I do believe there are more than two genders, just as there are more than two biological sexes. In my meager experience, rarely does anything or anyone fits into a neatly categorized binary.
In simplified terms, I define my bisexuality as being attracted to my own gender plus other genders. I really can’t imagine only being one gender exclusively, and in hindsight, a lot of my childhood crushes reflect this (even the ones I didn’t recognize as crushes at the time.)
To elaborate a little bit, I tend to be attracted to people on a person-to-person basis. I can’t quantify which gender I’m more attracted to, because it depends a lot on the person in question. In addition to physical attractiveness (I have a lot of really specific “types” I find attractive), personality and emotional depth plays a big part of it.
As such, I tend to be more attracted to fictional guys than I am real life guys, because they’re often more attractive and emotionally profound than most of the straight guys I know. Similarly, I tend to be more attracted to real life women than I am fictional women, because fictional women are less well-written and developed than the real women I know. But I have the potential to be attracted to people of any gender, provided I find that specific person sexually, romantically, and emotionally attractive.
The reason I don’t classify myself as pan (i.e. attracted to people regardless of gender), is because a person’s gender does make a difference to me in how my attraction towards them feels. I can’t explain it all that well, but feeling attracted to a guy, for example, is profusely different than being attracted to a girl, even though one isn’t necessarily less strong than the other. It’s just a different sensation.
I hope this helps!