From scifi.se's answer on similar question
Because Bucky was also frozen for most of that time:
Dialogue from The Winter Soldier makes it clear that Hydra put Bucky
back into suspended animation after completing each mission, and only
unfroze him when they needed him:
Zola: The procedure has already started. You are to be the new fist of HYDRA. Put him on ice.
Hydra Scientist: He's been out of cryo freeze too long.
Captain America: The Winter Soldier (2014)
Rest we have also seen from Captain America: The Winter Soldier and Captain America: Civil War that he has similar physical abilities like Captain America. So he also didn't aged like Captain America due to getting frozen. We also see few more humans treated with same Winter Soldier program in Civil War, which also didn't age a bit due to being in cryogenic sleep.
How Captain survived freezing has also been asked and answered below:
How did Captain America survive being frozen for 70 years in ice?