Bucky knew that eventually HYDRA would catch up to him, and they’d likely send Rumlow to round him up again. With more and more memories popping up everyday, he knew this wasn’t the first time he’d woken up from the brainwashing.
He also knew that Steve was now looking as well, and that couldn’t be allowed. HYDRA would only use him against Steve again, they’d never let him go. Thankfully the events following the rise and fall of Ultron distracted his best friend.
So he ran, he took jobs that no one else would since they didn’t ask questions. He squatted in houses to live off the grid. And he never stayed in one place twice, or too long. He’d even taken to carrying around an ipod and a pair of earbuds, figuring if he couldn’t hear the words he might have a chance to escape.
Eventually Rumlow caught up with him, and the ipod turned out to be a good idea. Bucky tried not to fight him, he did his best to escape but ended up taking several bullets. One through his right shoulder, the other two still stuck somewhere in his ribs near his upper back.
While scrambling across a rooftop dodging bullet fire Bucky literally landed on top of the avengers quinjet. While the entrance had perfect timing, now both of the people he was running from had found him. At least he knew who to side with, but getting away from Steve later would be a bitch.