Below are some links for a comprehensive "Bible study" about the doctrines and devotions of Catholic Marian theology. They also include many passages from the writings of early Church Fathers. I also highly recommend reading "Hail, Holy Queen" written by Dr. Scott Hahn.
The first 6 links establish a foundation for the Catholic doctrines pertaining to the veneration of Mary from both Sacred Scripture and Sacred Tradition.
Examples of scripture passages that impliclty/explicitly pertain to “devotion:”
1 Kings 2:19 - in the Old Testament Davidic kingdom the King bows down to his mother and she sits at his right hand. We, as children of the New Covenant, should imitate our King and pay the same homage to Mary our Mother. By honoring Mary, we honor our King, Jesus Christ.
John 2:7 - Jesus allows His mother to intercede for the people on His behalf, and responds to His mother's request by ordering the servants to fill the jars with water.
Matt. 2:11 - Luke emphasizes Jesus is with Mary His Mother, and the magi fall down before both of them, worshiping Jesus.
Luke 1:28 - "Hail Mary, full of grace, the Lord is with you." These are the words spoken by God and delivered to us by the angel Gabriel (who is a messenger of God). Thus, when Catholics recite this verse while praying the Rosary, they are uttering the words of God.
Luke 1:28 - also, the phrase "full of grace" is translated from the Greek word "kecharitomene." This is a unique title given to Mary, and suggests a perfection of grace from a past event. Mary is not just "highly favored." She has been perfected in grace by God. "Full of grace" is only used to describe one other person - Jesus Christ in John 1:14.
Luke 1:38 - Mary's fiat is "let it be done to me according to thy word." Mary is the perfect model of faith in God, and is worthy of our veneration.
Luke 1:42 - "Blessed are you among women, and blessed is the fruit of your womb, Jesus." The phrase "blessed are you among women" really means "you are most blessed of all women." A circumlocution is used because there is no superlative in the Greek language. Note also that Elizabeth praises Mary first, and then Jesus. This is hyperdulia (but not latria which is worship owed to God alone). We too can go through Mary to praise Jesus. Finally, Catholics repeat these divinely inspired words of Elizabeth in the Rosary.
Luke 1:43 - Elizabeth's use of "Mother of my Lord" (in Hebrew, Elizabeth used "Adonai" which means Lord God) is the equivalent of "Holy Mary, Mother of God" which Catholics pray in the Rosary. The formula is simple: Jesus is a divine person, and this person is God. Mary is Jesus' Mother, so Mary is the mother of God (Mary is not just the Mother of Jesus' human nature - mothers are mothers of persons, not natures).
Luke 1:44 - Mary's voice causes John the Baptist to leap for joy in Elizabeth's womb. Luke is teaching us that Mary is our powerful intercessor.
Examples of devotion to Mary from Church Fathers:
"Under your mercy we take refuge, O Mother of God. Do not reject our supplications in necessity, but deliver us from danger,[O you] alone pure and alone blessed." Sub Tuum Praesidium, From Rylands Papyrus, Egypt (3rd century).
"Recalling these and other circumstances and imploring the Virgin Mary to bring assistance, since she, too, was a virgin and had been in danger, she entrusted herself to the remedy of fasting and sleeping on the ground." Gregory of Nazianzen, Oration 24:11 (A.D. 379)
"Mary, the holy Virgin, is truly great before God and men. For how shall we not proclaim her great, who held within her the uncontainable One, whom neither heaven nor earth can contain?" Epiphanius, Panarion, 30:31 (ante A.D. 403).
"Hail, our desirable gladness; Hail, O rejoicing of the Churches; Hail, O name that breathes out sweetness; Hail, face that radiates divinity and grace; Hail, most venerable memory…" Theodotus of Ancrya, Homily 4:3 (ante A.D. 446).
http://scripturecatholic.com/blessed_virgin_mary.html#the_bvm-I
http://www.newadvent.org/cathen/15464b.htm
http://www.catholicapologetics.org/ap080400.htm
http://www.catholicapologetics.org/ap080300.htm
http://zuserver2.star.ucl.ac.uk/~vgg/rc/aplgtc/hahn/m4/ma.html
http://www.cin.org/users/james/files/key2mary.htm
The next 6 links are simply compilations of writings from the Church Fathers addressing official Catholic teaching. The 3rd link down specifically pertains to early Marian devotion, which specifically addresses the question of what the “pre-medieval” Church Fathers taught about devotion to Mary.
Examples:
"O noble Virgin, truly you are greater than any other greatness. For who is your equal in greatness, O dwelling place of God the Word? To whom among all creatures shall I compare you, O Virgin? You are greater than them all O Covenant, clothed with purity instead of gold! You are the Ark in which is found the golden vessel containing the true manna, that is, the flesh in which divinity resides."
Athanasius, Homily of the Papyrus of Turin,71:216(ante AD 373),in MCF,106
"Hail to thee Mary, Mother of God, to whom in towns and villages and in island were founded churches of true believers"
Cyril of Alexandria, Homily 11(ante AD 444),in CE
"O Virgin all holy, he who has said of you all that is honorable and glorious has not sinned against the truth, but remains unequal to your merit. Look down upon us from above and be propitious to us. Lead us in peace and having brought us without shame to the throne of judgment, grant us a place at the right hand of your Son, that we may borne off to heaven and sing with angels to the uncreated, consubstantial Trinity"
Basil of Seleucia, PG 85:452(ante AD 459),in THEO,187
"Hail Mary full of grace, the Lord is with thee; blessed art thou amongst women and blessed is the fruit of thy womb, because thou didst conceive Christ, the Son of God, the Redeemer of our souls"
Coptic Ostraca (AD 600),in CE (early form of the Rosary)
Anyone who has attended a Melkite Catholic Divine Liturgy (considered the highest form of prayer in Catholicism) has heard the liturgy that was formulated St. John Chrysostom and has been celebrated in the East since the late 300’s.
The liturgy is saturated with the utmost devotion to The Blessed Virgin Mary.
In the entrance prayers and 1rst 2 antiphons the following prayer is offered to God:
Deacon:
Remembering our most holy, pure, blessed, and glorious Lady,
the Theotokos and ever virgin Mary, with all the saints, let us
commit ourselves and one another and our whole life to Christ
our God.
http://www.ewtn.com/library/LITURGY/DILITSJC.TXT
One of the most devoted Church Fathers is St. Augustine. He is known for composing one of the most beautiful prayers to Mary in the Church (among many other great works):
Prayer of Saint Augustine to the Blessed Virgin
O blessed Virgin Mary, who can worthily repay thee thy just dues of praise and thanksgiving, thou who by the wondrous assent of thy will didst rescue a fallen world? What songs of praise can our weak human nature recite in thy honor, since it is by thy intervention alone that it has found the way to restoration. Accept, then, such poor thanks as we have here to offer, though they be unequal to thy merits; and receiving our vows, obtain by thy prayers the remission of our offenses. Carry thou our prayers within the sanctuary of the heavenly audience, and bring forth from it the antidote of our reconciliation. May the sins we bring before Almighty God through thee, become pardonable through thee; may what we ask for with sure confidence, through thee be granted. Take our offering, grant us our requests, obtain pardon for what we fear, for thou art the sole hope of sinners. Through thee we hope for the remission of our sins, and in thee, O blessed Lady, is our hope of reward. Holy Mary, succour the miserable, help the fainthearted, comfort the sorrowful, pray for thy people, plead for the clergy, intercede for all women consecrated to God; may all who keep thy holy commemoration feel now thy help and protection. Be thou ever ready to assist us when we pray, and bring back to us the answers to our prayers. Make it thy continual care to pray for the people of God, thou who, blessed by God, didst merit to bear the Redeemer of the world, who liveth and reigneth, world without end. Amen. (emphasis added)
http://catholicism.about.com/od/prayers/qt/Augustine_BWM.htm
http://www.cin.org/users/jgallegos/assumed.htm
http://www.cin.org/users/jgallegos/immac.htm
http://www.cin.org/users/jgallegos/mary_dev.htm
http://www.cin.org/users/jgallegos/theotok.htm
http://www.cin.org/users/jgallegos/venerate.htm
http://www.cin.org/users/jgallegos/virgin.htm
http://www.salvationhistory.com/library/category/apologetics
Also,the early reformers had a faithful devotion to Mary, and are perhaps good references for understanding Mary's place in salvation history.
"St. Paul says ‘God sent his Son born of a woman, These words which I hold for true, really sustain quite firmly that Mary is the Mother of God." -Martin Luther (Martin Luther’s Works, vol 7, page 592)
"A new lie about me is being circulated. I am supposed to have preached and written that Mary, the mother of God, was not a virgin either before or after the birth of Christ, but that she conceived Christ through Joseph, and had more children after that." -Martin Luther (That Jesus Christ Was Born a Jew, 1523, LW, Vol. 45, page199)
"Helvidius displayed excessive ignorance in concluding that Mary must have had many sons, because Christ’s ‘brothers’ are sometimes mentioned." -John Calvin {Harmony of Matthew, Mark & Luke, sec. 39 (Geneva, 1562), vol. 2 / From Calvin’s Commentaries, tr. William Pringle, Grand Rapids, MI: Eerdmans, 1949, page 215; on Matthew 13:55}
http://www.ewtn.com/library/ANSWERS/fr94101.htm
Catholics venerate Mary by keeping the commandment to "honor thy Father and thy Mother. Christians are the adopted sons and daughters of God. Jesus honored his Earthly mother perfectly. Catholics just follow in Christ's footsteps through the Biblically based Tradition of venerating Mary.