Yes, it is absolutely permissible and encouraged to shower during menstruation in Islam.
In fact, after menstruation ceases, performing ghusl (a complete ritual bath) is required before resuming prayers and other acts of worship. This act of purification is essential. The excerpt you provided reinforces this: "Remain away (from prayer) equal (to the length of time) that your menstruation holds you back. After this, bathe yourself." This highlights the importance of bathing (ghusl) upon completion of menstruation.
Why Showering During Menstruation is Permissible
There are no restrictions in Islam that prevent a woman from showering or maintaining personal hygiene during her menstrual cycle. Cleanliness is highly valued in Islam, and women are encouraged to maintain it even during menstruation. Showering helps maintain hygiene, remove impurities, and can improve comfort during menstruation.
Ghusl After Menstruation
Once the menstrual bleeding stops, ghusl becomes obligatory. Ghusl involves washing the entire body with water, ensuring that water reaches every part. This ritual cleansing is necessary to purify oneself before performing prayers, touching the Quran, and other acts of worship that require a state of purity.
In Summary
Showering during menstruation is permissible and encouraged in Islam for hygiene. A full ritual bath (ghusl) is required after menstruation ceases before resuming certain religious activities.