"—but bisexual in the way it’s mostly understood by society doesn’t quite fit either—"
Perhaps consider that how bisexuality is mostly understood by broader society is incorrect and that this would still falls within bisexuality? It's a spectrum (Kinsey scale), microlabels exist
i do think we need a label for “not a lesbian, but the chances of finding a man attractive are insanely low” because i am by definition not a lesbian but bisexual in the way it’s mostly understood by society doesn’t quite fit either and ik im not alone in that sentiment