Dear Anne: I understand where you are coming from, simply because I've been there myself. In the first chapter of "Behold Your Mother," I tell the true story of how I begged God not to let anything happen that I could take as a "sign" that it was OK to talk to Mary, if it was displeasing to Him that I do so. Three times I prayed this prayer. Three times my request to Mary was granted.
1. Because of the Incarnation. Mary's "yes" set the wheels in motion for the Word of God to come to earth and make it possible for us to be come children of God by adoption ... He is our brother, His Father is our Father, and He made His mother our mother as He died upon the cross (John 19:26-27). He continues to have that body in heaven (albeit in glorified form), and because of her obedience ... so shall we. She is our first and most perfect model of faith.
2. Because of the communion of the saints. Christians honor the saints both for their earthly example (including the writings many of them left behind to guide us) as well as their intercessions on our behalf. The Bible refers to the intercession of the saints in Revelation 5:8
When He had taken the book, the four living creatures and the twenty-four elders fell down before the Lamb, each one holding a harp and golden bowls full of incense, which are the prayers of the saints.
Similarly, our understanding of Mary's motherhood developed over time (in response to the Christological dogmas). In the fourth century, St. Ambrose wrote: "Let, then, the life of Mary be as it were virginity itself, set forth in a likeness, from which, as from a mirror, the appearance of chastity and the form of virtue is reflected. From this you may take your pattern of life, showing, as an example, the clear rules of virtue: what you have to correct, to effect, and to hold fast." (Concerning Widows, Book II, Chapter II).
Here we have the first reason to cultivate a relationship with Mary: to follow her example, just as we learn about how to be a wife and mother from our own mothers. As Mary's daughters, we try to emulate our mother especially in our eagerness to assent to every aspect of the revealed will of God.
Here I am, Jesus. I want to please You in everything I do, everything I think, everything I am. Because I love you, I want to honor those You honor, and love those You love. You love Mary, and I want to love her, too. I know that You perfectly fulfilled the Scriptures, and honored both your Father and mother. Show me how I can honor Your mother in a way that gives joy to Your Sacred Heart. Amen.