This is my perception of Sam in such a situation and this is how I picture their dynamic.
I still have a lot to learn but I hope I've done Sam justice in this fic and both of them in general.

Bucky walked quietly along the dock, he knew where he would find Sam.

When he reached the darkest part, he immediately spotted him. He did nothing to make his presence known and simply sat down next to Sam at the end of the boardwalk. He simply placed his hand on the small of his lover's back and waited.

"How did you know I would be here?" Sam asked softly.

"Joaquin texted me, he wrote me you couldn't save everyone. And I know that''s always where you come when something's wrong."

"You didn't have to come."

"I know Sam. The lake can't answer you, I can. So if you feel like talking I'm here and if you don't I'm just here for moral support."

Sam didn't answer and just leaned against Buck who tightened his arm around him.

After a few long minutes, Sam murmured, "Did Steve react like that too? Am I cut for this?"

Bucky placed a kiss on his head before answering.

"When Steve lost a man on the battlefield, everyone knew to leave him alone, he'd pound on a sandbag until his hands were bloody." Bucky took one of Sam's hands and kissed his knuckles before continuing, "I'm glad that this is not your way of reacting."

He paused for a moment before resuming, "As for being cut for it Sam, I'm more sure of it than ever, precisely because it doesn't leave you indifferent. Yes, you couldn't save everyone, it's not the first time and it's not the last. And you have the right to be upset, to be angry, to be sad, to cry, to react the way you feel. That doesn't make you a bad Captain America, on the contrary."

Sam whispered in a broken voice, "I don't want to be strong all the time."

"Hey, I'm a super soldier, I can be strong for two! Seriously Sam, I'm more and more aware of the responsibility Steve and I have put on your shoulders. And I know I've been acting like a selfish jerk.-"

"Bucky no..."

"Let me finish, I was being a selfish jerk, because there were a lot of things I never realized and didn't know. But I'm learning, and what I can tell you is that I'm glad you're the new Captain America, not because you've taken over Steve's legacy, but because you're the Captain America that people need now. So yes, you are cut for it, more than Steve would have been, because you are a child of this America. You understand it and know it better than anyone. That doesn't mean you have to be perfect or flawless, it just means you're the most qualified person to carry that shield with all that it entails. And the main thing you need to remember is that if the shield gets too heavy, you are allowed to put it down. Once you take off your suit, once you're here, you can let go Sam, I'm here, I'll always be here. You don't have to be strong 24 hours a day. Let us take over when you can't."

Bucky saw that Sam was opening and closing his fists sporadically. He tightened his arm around him and pressed it until Sam had his head against his chest. In response Sam breathed through clenched teeth and clutched Bucky's shirt as if he was holding on to the last branch before letting go.

Bucky whispered against his hair.

"Sam, Sweetheart, let go, I'm here, I've got you."

Bucky didn't know if this is what Sam was waiting for, but he felt his hands go slack and Sam's shoulders shake with sobs.

He just told him over and over, "Yeah Sam, let go, I got you." and continued to stroke his back and hug him.

Long minutes later, Sam had stopped crying and was breathing calmly against Bucky's chest. Then he slowly sat up, looked at Bucky and said, "Thank you," before kissing him gently. Moving back a little, he shook his head and had a slight laugh as if to mock himself. "I can't remember how long it's been since I've cried like this."

"At some point it has to come out Sam, you can't always keep it all in, and I'm glad I was there."

"I... I guess I didn't want to show you that side of me, because I was afraid it would make me a weak person."

"Hey Sam, having weaknesses, doesn't mean you're weak, just that you're human. What should I say, you've seen me at my worst, and you're still here. Do you realize how privileged I feel right now? Sam, you just showed me a side of you that you don't show to anyone, you trust me enough to let me see you in one of your most vulnerable moments. To me a former assassin, who tried to kill you, who treated you in the most violent way."

Sam took his hand and replied, "Of course I trust you, I love you, it's only natural that I trust you, and I know that man wasn't you and you're not him anymore."

"But still Sam, it's precious to me. So use it in the future, use me, don't control yourself because you think I only want to see the strong and brave Sam, no, I love you and I want you with all the packaging. Okay?"

"Okay, okay... you'll just have to give me a reminder once in a while, you know what they say, old habits die hard..."

Bucky laughed, "Darling, you're talking to a guy who is 106 years old..."

"Idiot" Sam replied fondly before standing up and reaching out to help Bucky up.

"Come on Bucky, let's go home."