Bucky had meant it when he said over the network that Natasha meant everything to them both. He didn't need to have all the details of what hers and Clint's relationship had been before they branched off into this being about the three of them to know that Clint felt that way about her, too. They both loved her, and they'd both be there for her through whatever came their way. If she needed to yell, to scream, to cry, even if she wanted to take out her frustrations by sparring with them. Bucky knew that Clint would do whatever necessary just as he would. They took care of each other; all three of them. The same way Clint and Natasha had shown up at his house even before they'd all gotten together, after his incident with Steve -- that's what this was, for her.
He liked that Clint kept hold of his hand. They were still sort of navigating through this development in their relationship and while it wasn't the focus of what was going on here, Bucky did like the way it made him feel. They were in this together, too. They would support each other while they supported Natasha. It's how they'd all get through whatever came up, be it this situation or anything in the future. It was a comfort; one he didn't realize how much he needed until they walked through the front door to find her.
And there she was, looking small and numb. Numb was a dangerous non-feeling. Bucky knew what it was like to be in that sort of state and it was not something he wanted for her. He'd rather her feel anything, even despair, than numbness. "That's not why we're here," he said, as they approached her together.
"We're here because you're here. We wouldn't be anywhere else."