The gemara says that two of the 18 gezeiros that were made by Chananya ben Chizkiya, were that one who immerses rosho v'rubo in drawn water after going to the mikva, and even one who has drawn water poured on them (even without going to the mikva), they become tamei. The rationale for this gezeira was that since people were bathing and showering after using the mikva, people began to think that it was the bath and shower that worked to make them tahor and stopped using the smelly mikva. Therefore, chazal had to forbid bathing and showering to prevent people from using a bath and shower as the mikvah.
Based on this concept, the Rama in the end of Hilchos Mikvaos (101), writes that some hold that after going to the mikvah, a woman shouldn't bathe or shower. The source of this Rama is the Ra'vya cited by the Mordechai in the second perek of Shavuos. The actual concern should apply equally to a tamei person and a Nidah to be permitted to her husband. Perhaps if a woman bathes after using the mikvah she will be misled into believing that it was the bath or shower that helped remove her tu'mah status. However, Rav Moshe (Igros Moshe Y.D. 2:96) points out that this opinion who forbids bathing for a Nida is only a da'as yachid. Technically, the gemara's gezeira only applied to Teruma because the entire nature of the gezeira was not that the bath or shower retroactively invalidates the immersion. Rather the nature of the gezeira was that it imposes a new tu'mah status on the person to make them passul from eating Teruma, as Rashi explains. Furthermore, the very fact that they extended this gezeira to one who has 3 lug of drawn water poured on them, which is not an act of tevila, clearly indicates that the nature of the gezeira was to impose a new status of Tumah on the person that was caused by the drawn water, not to invalidate the tevila in any way. Furthermore, even if it were to invalidate the tevilah, it was only said in the context of tu'mah, whereas the prohibition of a Nidah to be with her husband is a second consequence of becoming a Nida but not at all an outgrowth of her tu'mah status.
Therefore, Rav Moshe is confident that even those who extend this gemara to include a Nidah and say that if she bathes it somehow impacts the tevila and would prevent her from being with her husband, that is only if it is done immediately after the tevilah, or at least on the same day. But if a woman bathes 24 hours after immersion in a mikvah, there is no issue at all. Although in the gemara we find this gezeira extended even to a tahor person who is not going through a tevila process, that is because we are only invalidating him for teruma, but we couldn't possibly say that for a Nida, because if that would be the case it would always be forbidden for her to bathe. Even in the case in the gemara, Rashi 13b says that they only were gozer on one who bathed on the same day as the tevilah. Therefore, Rav Moshe assumes that the minhag would only apply for the duration of the day of tevilah, meaning the first 24 hours. For a woman who is very particular about not going 24hrs without a shower, he permits her to bathe or shower even on the same day as going to the mikvah since this opinion is only a da'as yachid and only a minhag which was accepted in situations that wouldn't cause serious discomfort.