The head or body bath( heavy bath using more water and for more time) during periods alters peripheral circulation so the uterus flow alters.. This will affect on next ovulation. The direct impact on babies skin if conceived in that month.
So the heavy bath is not advised in Ayurveda... so our ancestors followed same thing. Not only bath, even heavy meal, exercise, running, jumping, long talk, chatting, day sleep, night wake up, oil application, eye kajal application, make up's, too much combing, inter course like things are contra indicated to avoid the disturbance in menstrual flow.
Next Steps
Can wash body quickly with minimum water to maintain cleanliness, dont do Abhyanga( whole body oil application) before bath.