Both white and colored polyester fabrics can be safely bleached, as polyester usually has colorant added before the fibers are spun so that its colors are not affected by bleach. However, the item must not contain spandex, which can be damaged by bleach.
White polyester with stubborn stains or dinginess can be pre-soaked for better results. Add 3 tablespoons of bleach to 1 gallon of water, and then add garments, fully submerging them. Let the items soak for 5 minutes, then wash them normally with 1/2 cup of bleach and air-dry. For oily stains, the use of a pre-treatment applied directly to the stain before washing with bleach can be effective.