Although you can use conventional shampoo on colored or bleached hair, the color will probably fade more quickly. As the shampoo and hair dye react, this can also have strange and unwelcome side effects, including brassiness or other color changes.
Therefore, use a color-protecting shampoo while washing color-treated hair. A quality shampoo may extend your color’s life and keep your processed hair healthy. Search for a sulfate-free shampoo because sulfates can fade hair color.