Bucky may not be as purebred super soldier as Steve is, but she's still a fast healer. Banner lets her go after the burns have all but faded and he's convinced breathing smoke for a few minutes hasn't done any damage that won't clear up in a day or two, at most.

Except instead of going back to her rooms, she winds up at his floor, trying to decide if she should ask to be let in or not. (JARVIS, meanwhile, is a Bro and informs Steve that she's there before she can come to a decision.)