All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu 'alyhi wa sallam, is His slave and Messenger.
May Allaah The Almighty bless you and your efforts in the field of Da'wah (Islamic propagation). Please refer to Fatwa 4041 for the ruling on allowing disbelievers to enter the mosque. The summary of that Fatwa is that it is permissible to allow non-Muslims to enter any mosque - except for the Holy Mosque in Makkah - if there is a need for this, such as calling them to Islam.
However, when calling women to Islam, you should be very careful because women are one of the many trials for men. Therefore, when you speak to them, only speak about matters related to Da'wah. Also, you must not gaze at them and you should avoid being alone with a woman in a private place. It is recommended that if a man does call women to embrace Islam, he should be accompanied by his wife or any of his Mahram (unmarriageable kin) women. If this is not possible, a man should not sit with a woman in a place with a closed door, because when a man and woman are alone, they are in the situation where Satan would tempt them to sin. The Prophet, sallallaahu ‘alayhi wa sallam, stated this in a Hadeeth narrated on the authority of Ibn ‘Umar . [Ahmad and At-Tirmithi]
Allaah Knows best.