Bucky was friend of Steve Rogers before Rogers became Captain America. The movie Captain America: The Winter Soldier shows events 70+ years after that transformation. Captain America is so young because he was frozen for 70 years, and being a super soldier helped him survive (normal humans can't survive under frozen conditions).
Why hasn't Bucky aged like Peggy? If Zola needed to survive using cyberspace, it means HYDRA doesn't have the tech necessary to stop ageing processes.