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 ‘alayhi wa sallam, is His slave and Messenger.
First of all, it is not permissible for a Muslim to establish a relationship with a non-Mahram woman even if she is a Muslim, let alone if she is from the People of the Book. Therefore, you are obliged to repent to Allaah and immediately cut this relationship with this woman.
For more benefit, please refer to Fataawa 82885 and 81356.
You did well by calling her to Islam, and you are not sinful for insisting on calling her to Islam, however, we do advise you to avoid her in order to be safe in regard to your religion and dignity.
It is permissible in Islam for a Muslim man to marry a chaste woman from the People of the Book, however, we do not advise you to marry any such woman even if she is chaste, because there are many disadvantages in marrying women from the People of the Book especially about the religion of the children.
For more benefit, please refer to Fatwa 84159.
Allaah Knows best.