All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
It is not permissible for a Muslim man who fears Allah and prefers His Obedience to everything to have an affectionate relationship with a woman, except with his wife. So, dear brother, you have to get rid of such a relationship before you invite her to Islam. From the Sharee'ah point of view, know that you are not allowed to help her touch the Quran since she is not a Muslim.
Allah Says (what means): {Indeed, it is a noble Quran. In a Register well-protected. None touch it except the purified.} [Quran 56:77-79]
After that, we advise you to send her some cassette tapes that introduce Islam and its good features.
Allah knows best.