Flea control in cats has traditionally used collars, these are often the cause of injuries to the arm pit and rarely control fleas adequately. Many people buy pet shop products, but these can be more toxic to the cat than the fleas. The best method of control is by using something like frontline or advocate which is proven to kill fleas not cats.
Spraying the bedding is essential but avoid buying small bottles of spray, you will need approximately 500ml of spray to treat a house. Washing bedding will have no effect except to clean the fleas unless you use a boil wash.