Mr. Bucket appeared in Roald Dahl's novel, Charlie and the Chocolate Factory, but he didn't make a film appearance until 2005's Charlie and the Chocolate Factory.
Charlie's father works at the local toothpaste factory attaching caps. He works for many hours, the pay is terrible, and very occasionally there is unexpected surprises.
He is eventually replaced by a machine and left jobless.
He gathered broken lids and brought them home for Charlie which he made into a miniature factory with Willy Wonka present.
Mrs. Bucket is believed to be the son of Grandpa George and Grandma Georgina and as paying to attention to film you can notice him address Grandpa George as Pops, implying their relation.
"Whatever happens you will still have the candy"Edit
In the end Charlie's father ends up in the factory supplying food and gains a better job as the man fixing the machine that replaced him.
His pay then increased tremendously supplying the good food for the family in the end.