Bill had always trusted Bucky, he'd trusted him as children, during the war, heck he'd even trusted him as The Winter Solider, to see him and for their bond to be enough to bring him back. So when he told him they were okay, Steve was going to believe him. That's what he wanted, that's what he'd always wanted. Bucky deserved a life, after everything he deserved the warmth and safety of real love and maybe he'd found that.
It was unconventional and Steve was going to worry, it was what he did best, but he wasn't going to judge. Bucky was an adult now, not a wayward youth and trusting him meant that Steve was going to trust his choices. Even then it didn't really matter what he thought, this was something that had nothing to do with him and that was going to take some getting used to because usually Bucky and his life were exclusively Steve's business. Their relationships, all of them, had changed and shifted and losing things left room for new things.
"We're always okay," Steve assured him as he reached out to lay his hand on Bucky's shoulder and gave a firm squeeze. It warmed his heart to see the two dogs, maybe just what they needed right then, something light. Things between Bucky and Tony were a disaster and Natasha was cold and distant toward him in a way Steve couldn't fix, but he hoped that wouldn't hurt a bond that had survived lifetimes.