Choose a cream bleach for facial hair. Cream bleach is appropriate for lightening hairs that are not completely black, just dark. It lasts for up to 2 weeks. Be sure to only choose bleach that is recommended for use on the face; since the skin here is so sensitive, you have to be extra careful to avoid irritation. Don't go in the sun for 24 hrs after waxing to prevent your upper lip from getting a dark pigment. 2  If you happen to be a girl that has enough upper-lip hair that you feel you must do something about it, consider using tweezers to remove the hair. 3  It is an easy process to master with just a bit of practice.