bicrushual
You're not necessarily bisexual, you're not necessarily bi-romantic, merely bi-crush-ual. You find yourself crushing on, or infatuated with, a person or persons of a sex or gender whose persons you don't find yourself interested in doing anything sexual or romantic with; you're merely crushing on them.

Doesn't necessarily rule-out being heterosexual or hetero-romantic (sometimes mashup-spelled heteromantic), but would seem to rule-out being strictly hetero-crushual.

Potential alternative terms: bi-infatual; bi-infatuated.

As with all of these matters, you can be a little, a lot, or totally, bicrushual. (Demi-bicrushual?)

Similarly, you choose how you identify yourself. Every rule has exceptions! (Except this one.)

(According to Google, appeared on the Internet for the first time on 3 April 2010 @ a blog with which I have no connection.)
Straight-identifying starlets who tell talk-show hosts they have a girl-crush may or may not be bicrushual.