Straight lemon juice -- squeezed directly from the lemon or poured from a bottle -- works very well for bleaching and doesn't contain the harsh and potentially-dangerous chemicals the name brand bleaches do.
Just about any fabric (except silk) can be bleached a whiter and brighter color by soaking in a mixture of lemon juice and very hot water. First, mix 1/2 cup lemon juice with 1 gallon very hot water. Soak the clothing in it for at least one hour, though it can soak as long as overnight. Afterward, pour the lemon juice mixture into the washing machine, then wash the garment as usual.
As a bonus, your clothes will have an extra scent of freshness!
Adapted from "101 Old-Time Country Household Hints," © 2008 Publications International, Ltd.