A tampon may have the status of a chatzitzah for a woman immersing in a mikveh for conversion, so it should not be inserted for the immersion. However, a tampon (or any other sanitary product) can be used before and after, removed just for the immersion itself. A bit of wet menstrual blood on the body is not considered a chatzitzah.
If the woman is bleeding enough that there are sanitary concerns for mikveh, or if she would feel embarrassed, the immersion should be pushed off for a time when the bleeding is lighter.
Please write back with any further questions.