Bucky's character is absolutely and wholly a joke in this series. He is just a second "Loki" type of the witty dark bad guy working with the good guys now, and his past only comes up when it needs to (not to mention it being completely forgotten when it is needs to be). It simply doesn't match with his character anywhere else in the other films.
To be fair, this is only the first three episodes. But the plot is fuzzy, the characters have no real substance, and I don't see where they're taking the show. The characters are pawns for whatever plot may exist rather than made to be people.