As far as  Shari`ah is concerned, a non-Muslim wife is not required to abide by the Islamic Shari`ah-related matters such as “intention” or following the exact method of performing ghusl. Therefore, as long as she has taken a full bath after being purified, there is nothing wrong in having sexual intercourse with her.

The prominent Muslim scholar and d a`iyahZeinab Mostafa states: Practically she has purified herself and she is no longer menstruating.

As for the niyyah and proper Islamic way of making ghusl, these are Shari`ah-related matters that she is not required to do since she is not a Muslim.
Therefore, there is nothing wrong in having sexual intercourse with her as her husband as long as she has taken a complete bath.