It is not advisable to perm hair that has been bleached because the chemical process can damage and dry the hair; bleached hair has already been damaged by breaking the bonds in the hair and raising the outer cuticle. Modern perms will allow you to dye colored hair, but you would need to discuss this with your hairstylist beforehand to establish the condition your hair is in. You cannot color your hair for at least ten days after it has been permed because dyeing your hair will open the outer follicle.