A woman about to immerse in the mikveh for conversion does not have to be concerned about where she is in her cycle and does not do bedikot etc. She simply has to be sure that there are no barriers (chatzitzot) between her body and the mikveh water. Therefore, she bathes, combs her hair, and generally prepares for mikveh in the same manner as a Jewish woman immersing for niddah purposes.
Any bleeding a woman experiences before her immersion for conversion does not render her niddah. This is true even if the bleeding began once her conversion was already approved. Therefore, once she immerses for conversion she is tehorah until she next experiences bleeding.
If a woman is actively bleeding at the time of her scheduled immersion, and feels uncomfortable or embarrassed, she can ask for her immersion date to be postponed.
If a woman is planning to get married shortly after the conversion, she may be required to count seven clean days and immerse again (after completing the conversion) due to the concern of dam chimud (as any bride must) depending on the specific circumstances. If this is the case, please get back to us with more details (are both spouses converting or just the wife, were they previously married in a civil service/living together). Alternatively, the couple can clarify this detail with the rabbi who will be performing the marriage.
Please feel free to get back to us with any further questions.
B'Hatzlacha!