"If Mary is the new Eve, then that would mean she is the bride of the New Adam, Jesus."
Correct - spiritually she is His bride as well as His mother, for she is also both a type and Mother of the Church.
"How does Mary fulfill any of the typology of Eve? "
What does the word "Eve" mean?
"If Mary is the new Eve, then that would mean she is the bride of the New Adam, Jesus. But not even you guys believe that. Your typology makes no sense if she is new Eve. How does Mary fulfill any of the typology of Eve?"
According to Genesis 3:15, the New Eve was to be the mother of the New Adam: "I will put enmity between thee and the woman, and between thy seed and her seed."