William 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.
He was played by Noah Taylor.
William worked at the local toothpaste factory screwing on caps. He worked for many hours, the pay was terrible, and very occasionally there were unexpected surprises. However, due to rise in cavities resulting in a rise in toothpaste sales, the company made enough revenue for the factory to modernize their factory by adding a machine putting caps on the toothpaste tubes, thus laying him off and leaving him unemployed.
He gathered toothpaste caps and brought them home for Charlie which he made into a miniature factory with Willy Wonka present.
William 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 Pop, showing their relation.
"Whatever happens you will still have the candy"
In the end William ends up in the factory supplying food and gains a better job as the man fixing and maintaining the machine that replaced his previous job. His pay then increased tremendously supplying the good food for the family in the end.