They were a package deal. Inseparable, despite being separated for decades. They were always going to have a connection, a bond. That didn't go away no matter what the context of that bond actually was. Their partners were good about it in that they could recognize it was something only Steve and Bucky really understood and so they didn't try -- they just accepted that it was there and let it be. Bucky was forever grateful to Clint for that -- and honestly? To Tony, too.
"I can't imagine he'd say no," Bucky said. But then, Stark was kind of unpredictable. Bucky could see him thinking he wasn't good enough or some other self-deprecating reason for not thinking he should be marrying Steve. Bucky understood that; he still got like that sometimes before he received a sounding thaw on the head from his husband to get his head out of his ass. Hopefully Tony wouldn't go down that path. They were practically living as a married couple with two kids already. The American Dream at its finest.
"I think it just being the two of you is a good plan. Something intimate, small. But it'll be special, for you two to remember. Is there anything you need besides the ring? Anything I can do to help? Besides keeping Tony the goat from screaming during the big question."