Just as Tony had thought to wait, so had Bucky. When the illness he had seemed to wear off and his muscles grew back to the size he'd gotten used to, Bucky had been wary and unsure whether it was smart to act on it right away or not. What if it didn't last? He didn't want to go through the trouble of Tony having to put the arm back on only for him to have to take it right back off. Shuri was there now, and possibly could help him with it moving forward but he didn't want her to have to worry about it either. It wasn't until Clint convinced him that the sickness was gone and Bucky wasn't going to revert back to his former self again anytime soon that he finally conceded to the idea of going to see Tony again.
They had apparently been on similar wave lengths because just before he was going to seek out Stark, he'd reached out to him instead to see if he wanted the arm back. After a brief exchange, they agreed to meet at his workshop to do it. This time, without their significant others to babysit them and make sure they didn't get into a scuffle.
Bucky had no interest in fighting Stark, or stirring anything up between them. He doubted they were going to walk away from this the best of friends, but he did hope they could get along. It'd make things easier for Steve, anyway. He approached, keeping quiet until Tony acknowledged him.
"Hey," he said in return. "Thanks, for agreeing to meet with me to do this. Should I sit somewhere?"