If I'm reading you right your question is not really specific to Rome but more the ancient world in general. Menstruaton is a Very Big Deal in Zoroastrianism, so I touch a bit on it in my writeup on women's status in pre-Islamic Iran.

To briefly answer your questions more directly: menses entailed an extended period of ritual impurity and would generally prevent a woman from carrying out household duties or engaging in sexual activity. She would be expected to seclude herself and engage in ritual cleansing, so the flow of blood was presumably managed by intermittent cleaning. To what extent this was done in practice is unclear, but Jahi, the hypostasis of menses, is associated with droughts and withering (= opposite of nourishing flow of water) so field work for example was probably taboo.

Menses were considered an artefact of our imperfect bodies, a permanent wound of sorts, ultimately resulting from Ahriman's assault on Ohrmazd's perfect creation. While women and men were both imperfect, the long duration of menstruation (compared to ejaculation, to some extent seen as the male counterpart) was often taken to suggest a weakness and susceptibility to evil inherent to the female aspect of humanity; conversely, the perfect primal man Gayomard is explicitly masculine, if not male in the strict sense, humanity having sprouted from his semen spilled into the earth as he was slain by Ahriman.