All of what you say is true, however, there is one other important mitigating factor: the coloring of the cloth is Derech Lichluch. In other words you are spoiling the cloth with the coloring.

See the Shulchan Aruch (OC 320:20) - in the name of the Sefer Yere'im - that says that it is forbidden for one to wipe the colored fruit juice from his mouth with a napkin because he is coloring the napkin. The Mishnah Berurah, however, brings a number of Poskim that disagree with this Psak and hold that Tzove'a Derech Lichluch is permitted l'Chatchilah. The Mishnah Berurah's final Psak is that one can rely on these Poskim if there is no alternative. Since it is not possible for a woman to make a Hefsek Taharah any other way, it should be permissible for her to do it.

Furthermore, the Shulchan Aruch ha'Rav adds that even the Sefer Yere'im is lenient about coloring Derech Lichluch if it is not customary to color this type of cloth. So, for instance, it is permissible to put a gauze bandage on a wound even though it will be colored by the blood. The pieces of cloth used to make a Bedikah are specifically not colored and therefore it should be permissible to make a Hefsek Taharah on Shabbos according to all opinions.

b'Chavod,

Yonasan Sigler

This is not a Psak Halachah