Washing colored clothing with light colored clothing runs the risk of the colors bleeding onto each other. The darker dyes might discolor the white fabrics, leaving an unpleasant stain that can cover the whole shirt. However, not all hope is lost. There are a few methods that could remove the blue dye and salvage the white shirt.
Fill the kitchen sink with lukewarm water. Add 1/4 cup of heavy-duty liquid detergent. Mix the water and detergent together with your hand. Submerge the shirt into the water. Agitate the water and shirt to mimic the motion of a washing machine for several seconds.
Drain the sink and rinse the detergent from the shirt with cool water. Fill the sink with cool water and pour 1/2 cup of color-safe bleach into it. Submerge the shirt into the mixture and allow to soak for 30 minutes.
Remove the shirt and allow the sink to drain. If the blue dye is still visible on the white shirt, fill the kitchen sink with lukewarm water and add 1/2 cup of chlorine bleach. Submerge the white shirt in the mixture and let it soak for 15 minutes. Drain the water and rinse the mixture off the shirt with cool running water.
Examine the white shirt. If the dye is still visible, do not continue to soak the stain with bleach. Doing so will weaken the shirt's fabric. Instead, you will have to replace the item.