Amy is a girl who has lived way past her time, and by that I mean, she's a 99-year-old, in a 30-year-old's body. She was half of Hydra's pride and joy, their elite killers.
The Winter Soldier, and The Summer Assassin.
He had a metal arm and she had a severe case of pyromania, as in, Hydra had given her fire-wielding abilities that couldn't be explained. That wasn't the only change, her hair had turned into a fiery red colour, sometimes lighting up completely, and her eyes burned like the sun.
She was very different from the soldier, but there was one thing they both needed the other for, comfort. Only they knew the pain they had suffered through, the torture, the loss, the guilt they carried day to day. It would never fade, Hydra would always be a part of them...
Bucky may have been found and is being helped, but there were others with him. While regaining his own memories, he see's a specific girl fighting against him with HYDRA. She's fast, strong, and silent, just like him.
He may not remember much, but he does know that he wants to save that girl from what the rest of HYDRA is doing to her. While they plan on how to get her to safety, they meet her outside in the streets. She's masked from the eyes down and she's ready to kill. After seeing and fighting her, Bucky remembers more about her than he thought there was to remember.
He found that feelings sprouted inside the seemingly emotionless Winter Soldier, and maybe in the other soldier as well.