the_genderman

Canon divergent. Bucky got the off-brand serum, so it doesn't do as good a job healing his injuries. But HYDRA don't care, they run him until he "breaks" and is no longer efficient enough, so they stick him back in cold storage and pretty much forget about him.
Then, after the Triskelion and helicarriers, when Natasha dumps the SHIELD/HYDRA files, she finds something about the Winter Soldier (who, in this AU, she had never met before or seen), and recognizes him as Sgt Barnes from SHIELD's wall of fallen agents. She tells Steve. They and Sam find him, maybe the rest of the Avengers are involved, too. Whatever powers that be want to use Steve's serum to get him back into fighting shape, because he could be so useful to help take down HYDRA. But Bucky doesn't want to fight any more. He's not thrilled with the chronic pain, but he prefers it to being a weapon again. It's his body.
Maybe he runs away again, and Steve has to come to terms with his decision to not get cured. And find him again.

Later edit: I can see Steve needing some time to come to terms with why Bucky wouldn't take the opportunity to not live with pain, because he knows what it's like. Maybe he thinks Bucky's trying to "punish" himself for what he did as the Winter Soldier. Maybe Bucky kind of is trying to "atone" through pain. Maybe it's a highly experimental idea/thing about how to use Steve's serum to possibly help him, and he doesn't want to do it if it's possibly going to hurt Steve, hurt him even more, or simply not work.