All perfect praise be to Allah The Lord of The Worlds and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
The woman in menstruation is permitted to recite a verse, part of a verse or verses from memory, such as Āyat al-Kursī and both Surat Al-Falaq and Surat A-Naas (two last 'Qul' surahs). This is because the purpose, here, is fortifying herself and not reciting Quran. It is as if she said: "Bismillah al rahman al Rahim" or " Inna lillahiwainna ilayhi raji'un." However, if her heart wasn`t at ease, then she can say other du‘ā, such as "A`oudhou bikalimati l-Lahi t-tammati min charri ma khalaq" and " BismI-lahialathi la yadiroMa`aIsmihishai` fi ilArdiwa la fi Al-Sama`WaHwa Al-Samei Al-Aleem."And Allah knows best.