Yandere Bucky tends to fall into a few really distinct patterns, which honestly makes sense given his character history. The whole Winter Soldier programming and conditioning provides this built-in justification for obsessive, possessive behavior that feels way more organic than in other fandoms. You see a lot of stories playing with the idea of the reader being a handler or a mission, and the 'completion' of that mission somehow morphing into a twisted form of devotion. The Asset doesn't let go of its objective, basically ever.
Another huge one is the protective yandere angle, especially post-WS recovery. Bucky decides the reader is his new tether to sanity or his reason for staying 'good,' and any perceived threat—whether Hydra, other Avengers, or just a nosy neighbor—gets met with extreme, quiet violence. It's less flashy madness and more chillingly competent elimination. The dynamic often hinges on the reader's awareness; is she scared, or weirdly complicit? That tension drives a lot of the best fics.
I'm less into the versions where he's just randomly crazy from the start without that narrative scaffolding. The appeal for me is the specific blend of lethal capability, trauma, and a loyalty that's been horrifically distorted. It's not just 'he's obsessed,' it's 'the Winter Soldier's target acquisition protocol never disengaged.'