In 'A Christmas Story', the main bully is Scut Farkus. He is a mean kid who likes to pick on others, especially Ralphie and his friends. He has a sidekick named Grover Dill, who also joins in on the bullying.
In some Christmas stories, the innkeepers who turn Mary and Joseph away could be seen as 'bullies' in a sense. They were not very kind or accommodating, leaving the couple with no proper place to stay just when Mary was about to give birth.