I realize that the comic version had a EMP, which the movies have taken out. However, Bucky has been shown to block bullets with his arm,indicating he has something to attract them toward the arm rather than his body. In addition, Black Widow's disk/pin was able to disable the arm in TWS. I would assume yes, but is there any confirmation for this? Anything works, I don't care as long as it's canon.
I may be wrong and his bionic arm might have some electromagnetic capabilities but all i can find is his abilities and skills.
From MCU Winter Soldier:
Enhanced Speed: Winter Soldier's speed is is enhanced beyond the peak of human potential, moving into the early levels of superhuman condition. Bucky's speed is comparable to that of Captain America, who can casually run at 30 miles per hour with ease, and still had trouble keeping up with Barnes.
Enhanced Agility: Winter Soldier's agility is superior to that of an ordinary human. He has demonstrated the ability to leap on top of midsize cars in a single bound and do acrobatic flips avoiding gunfire into cover.
Enhanced Reflexes: Winter Soldier's reflexes are enhanced to extraordinary levels. His reflexes are responsive enough to catch Captain America's shield being thrown at him at a high velocity. He was also able to catch enemy grenades thrown at him, dodge fire from Falcon's Steyr SPPs, and leap on top of a moving car accelerating towards him with pinpoint accuracy.
So with the serum (that had a similar effect on the human body as the Super Soldier Serum given to Steve Rogers) and a LOT of luck is the explanation I can come up with.
Side note: If Bucky had a strong electromagnet in his arm, any bullets affected by the magnet would stick to his arm. This would be easily seen in the movie if it was the case.