He collects Zemo's bowl once he's done and brings them both to the sink. For all the evident self-neglect and the way the state of the house seems to reflect the state of his mind, Bucky is still keeping a few self-care habits. He still dutifully keeps the sink empty instead of letting dishes pile up. He still showers and grooms himself. Brushes his animals and try to feed them on a more regular schedule than he feeds himself. Maybe not all is lost yet.

"I need to do some work in the barn. You can go get a bed and whatever else you need or move your car in." No, Bucky isn't intentionally trying to help Zemo. He doesn't want any more unwanted guests showing up or to be implicated in whatever shit Zemo got himself into, that's all.