He sleeps well enough. He won't have any complaints about it, not that he would anyway, but it's sleep and sleep in a place he's not liable to be attacked unless Tony changes his mind. It's been awhile since he's managed it so unless Tony wakes him it'll definitely be few hours before Bucky stirs again.

When he wakes up, he runs through what he knows. His name. Steve. The events leading up to now. Tony. He remembers everything since the Helicarrier and it's a relief. He sits up, still in the robe and looks to Tony for directions.