Doing Hefsek Taharah on Shabbos:
[Being that washing only minority of one’s limbs with water heated before Shabbos is permitted,] therefore in a place where there is no [accepted] custom [otherwise], a woman is allowed to begin her seven clean days on Shabbos, being that [to do so] she only needs to wash her private part and between her thighs. However she must be careful not to wash with a cloth so she not come to squeeze it. [She may use either cold water or warm water that was heated before Shabbos for the purpose of this wash.]
A woman may clean her area for a Hefsek Taharah as doing so is only washing minority of one’s body
 After a married woman menstruates she must separate from her husband until she has counted seven clean days, meaning days that she has not seen any blood. To begin the count she must wash herself the afternoon prior to her wanting to begin the seven day count and then check herself to verify that the blood has stopped flowing. Thus this washing may be done on Shabbos in order to have the first of the seven days begin after Shabbos.
 Kitzur Dinei Taharah 4/7