Praise be to Allah, and may Allah’s peace and blessings be upon the Messenger of Allah, his family and his companions.
As to what follows:
In response to your question, we say, and with Allah Almighty lies all success:
In relation to bathing with water while she is menstruating, or bathing with water that has been recited upon (with Qur’anic recitation), while in the washroom, then this is of no harm. That is because this water does not earn the quality of prohibition of being used in its usual ways; just as Zamzam water, which is blessed water, as in the Prophetic statement, “Zamzam is the food of nourishment and the cure of disease.”
However, even then, the correct opinion amongst the scholars is permissibility of using it in bathing and using it even if it passes through the drains in the washroom. So there is no harm in this, and there is nothing that prohibits using water in this way. So if the water was recited upon, then it is blessed from the aspect of being recited upon. But this does not prevent it from being used in bathing, whether the woman is menstruating or in the washroom. I do not know of any evidence from the Qur’an or from the Sunnah that the water is preserved if it is recited upon, or that water is safeguarded, due to its being Zamzam, from bathing in it.
Having said that, there are some sayings of the Companions regarding the issue of bathing with Zamzam water, but none of these sayings are related from the Prophet (peace be upon him).
And Allah knows best.