Bucky ditches Hydra after hearing about Tony going missing in Afghanistan. I dont think he saves him but once Tony is home he hides him in the Miami mansion. They at least knew each other before the escape.
There's also something with a fridge. Sorry. Maybe Bucky breaks it or hides behind the open door. Probably not the last one but I am just guessing.
Ooh and if I am remembering the same fic Bucky helps in the background during the Stane incident.
Found on the winteriron finding tumblr blog. It's a 3 part series called Just Give Me a Reason by naturalchoas on ao3.
The first story is winteriron but it turns to stuckony in the last 2.