A Mouth Like Genocide

Is it one of the psychosexual connections Bullseye has? Yeah, the two instances they have clashed.

Bullseye has a competence kink when it comes to violence, Gambit is very competent and only scratches by against him, aka 1 win and 1 loss (allies scared Bullseye away from killing him), and that's WITH mutant powers of explosion. So they are pretty even and they both fight in a very agile and calculating way: using their environment and looking for weakness. Bullseye would appreciate that.

So yeah, Bullseye would be turned on by fighting Gambit, and Remy probably dislikes/fears him pretty much even if he acknowledges his competence.

I can only see it in a noncon/dubcon fashion from their dynamics. Maybe younger (pre marriage) Gambit might have seduced Bullseye as a honey pot to then betray/beat/steal from him, or some other scenario that tickles your fancy, like Lester getting fixated on him and doing the whole ambiguously gay nemesis and fixation business. But current era it's a big no in compatibility and Official Sexual Preference status. But for fandom purposes, go have fun. No fics on AO3 yet, but that's never stopped anyone.

Imho, an AFAB Bullseye would want to transition to male. In my head, the concept of Bullseye is such a masculine one, with all the toxic masculinity, that it's not really squaring with femininity but if we're staying there: she'd be such a butch -- in a bordering misogynistic fashion.

Angry scrappy kid, often mistaken for a boy grows into an athlete who works out way too hard and either crops her hair or keeps it in the most utilitarian way possible. Force her into a dress and she looks like it's the most unnatural thing possible.

Military career, even more masculinity and order: trying out of sheer spite not to show how ~emotional~ she is as the bipolar disorder gets out of control. Her anger and highs are deemed hysterical and she grits down even harder: costumed life gives a bit of a reprieve. No relationships, a loathing at the very thought of motherhood or house wife life. If she has a sex life, she sterilizes herself. Not quite self-aware that she might not identify as female, as that doesn't really exist in her head (but if it had she'd transition asap).

Still the psychosexual connections to violence and her enemies, but being a woman it'd go even further on the sexual bit on her enemies side, excepting Elektra and their rivalry would be even more the center of Bullseye's existence.