OR: Natasha standing there, all deadpan and she says "Do you recognize me now, or do I have to hit you over the head again?" And Bucky just looks kinda terrified for a second but says "Nope, I'm good. Wanna go grab some dinner, Natalia?" And she replies, "About damn time. I thought you'd never ask James." And they live happily ever after!!!!!
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.