I think that if she is to be a bride of Christ she had better be a virgin or she will not take part in the first resurrection.
I understand what you are saying in that you are comparing Eve to the church and how could she be a virgin if she had sex with Satan. Eve is not the church. She is the mother of all living because Christ would come through her and if you believe in Him you will have everlasting life. Through her also came Cain and if you follow his father you will be judged to hell.
Churches may teach that Eve is the church but I have not yet found it in scripture. It may be, but I have never seen it. Until I do I will continue to believe that is one of the traditions of man.
When you say, "the bride of Christ is a virgin" it isn't speaking about a church but rather those that remain faithful (do not commit adultery with the anti-christ). They do not fall for his deceit at the end of days. That is how this "type" of virginity is maintained. Staying true to our Saviour.
......Ping