Natasha has a habit of coming up behind Bucky and putting his hair up for him whenever he's doing something and his mop of hair gets in his eyes. Whether he's trying to figure out the computer or eating or bickering with Steve, she'll just sidle up behind him and pull his hair away from his face in a little half-bun, and he just holds still until she's done because, honestly, everything is so much easier when he can see.
She does know from experience. He trained her in the Red Room. He doesn't remember her, and we've seen no evidence in the MCU that she remembers him from the Red Room, but these two DO know each other.
I hate this and the worst part is, I think this is probably what the good old days were like--Bucky being a hit with the ladies and dancing and having a grand time, while Steve watches longingly on the sidelines. But he'll never mention it to Bucky because he doesn't want his brother to know how jealous it makes him, it's a silent division.