Timeframe: Mid 4th century onwards
If by "the Bible" you mean the Bible as we have it in its current form (albeit in some cases missing the Deuterocanon), then the time period we must consider is from the mid-4th century onward. The first enumeration of the books of the Bible we know of by any Church Father is that of Athanasius of Alexandria (ca 296-373) in his 39th Paschal Letter, written around 367 AD. The first local Church Council to formalize the canon was the 3rd Council of Carthage in 397 (in Canon VI). The canon of Scripture would not be formalized for the entire Church (i.e. all five ancient Sees - Rome, Constantinople, Alexandria, Antioch, and Jerusalem) until the 7th Ecumenical Council in 787.
The majority of Christians learned about the Bible from Church services
It is sometimes overlooked that the motivation for creating a canon of Scripture in the first place was to normalize what was being read in Church. The canon established by Carthage described the books of the Bible as those which "must be read in the Church." Athanasius wrote at the end of his list of books that he was directed "by the need and advantage of the Church."
The canonization of Scripture for Christians more or less coincides with the formalization of written Church services. In the east these include the Liturgy of James, the Liturgy of Basil, and the Liturgy of John Chrysostom, all of which date from the mid to late 4th century (although the Liturgy of James is thought to have roots dating to the 1st century).
What all first millennium Liturgies had in common - east and west - was a portion called the Liturgy of the Catechumens (sometimes called Liturgy of the Word) and a portion called the Liturgy of the Faithful (sometimes called Liturgy of the Eucharist). The Liturgy of the Catechumens was that portion of the Liturgy devoted to reading and expounding on Scripture, including a Gospel reading, an Epistle reading, and several excerpts from the Psalms. Its origin is in the Temple and synagogue services of the 1st century, which the very earliest Christians continued to attend (see, e.g., Acts 2:46;3:1). The very term "the Bible" (Greek τὰ βιβλία - tà biblía) was coined by John Chrysostom, Archbishop of Constaninople, during one of his homilies on Matthew, sometime around 386 (biblon, the singular, was a nickname given to a bound collection of papyruses - named after the Phoenician port of Byblos where many such papyruses originated).
The Church adopted a cycle of readings that repeated each year. A lectionary of Gospel and Epistle readings for Saturdays and Sundays may have been in place as early as the 2nd century, according to some scholars.1 Weekday readings were added later. The eastern (Orthodox) Churches today and western churches following the eastern rite continue to use an annual Gospel and Epistle lectionary that is probably well over 1,000 years old. Many of the writings we have of various Church Fathers are commentaries on these same Lectionary readings. John Chrysostom's homilies on Matthew, John, Acts, and the Pauline Epistles are one example. An example from the west would be the collection of Gospel homilies by Gregory the Great. Although later transcribed, all of these would have been intended originally to be heard, not read. (In some of John Chrysostom's homilies he even scolds people for going to chariot races rather than to church).
A sense of how pervasive Scripture was in early Christian Liturgy is found in Kallistos Ware's description of the eastern Church services:
During the course of Matins and Vespers the entire Psalter is recited each week, and in Lent twice a week; Old Testament readings occur at Vespers on the eves of many feasts, and at the Sixth Hour and Vespers on weekdays in Lent ... The reading of the Gospel forms the climax of Matins on Sundays and feasts; at the Liturgy a special Epistle and Gospel are assigned for each day of the year, so that the whole New Testament (except the Revelation of St John) is read at the Eucharist. The Nunc Dimittis2 is used at Vespers; Old Testament canticles, with the Magnificat3 and Benedictus4, are sung at Matins; the Lord's Prayer is read at every service. Besides these specific extracts from Scripture, the whole text of each service is shot through with Biblical language, and it has been calculated that the Liturgy contains 98 quotations from the Old Testament and 114 from the New.5
The earliest visual aids: Icons
Statues and stained glass have already been mentioned, but icons and mosaics are almost certainly the oldest non-verbal means of presenting and explaining Scripture. Eastern and western Church tradition holds that the Evangelist Luke himself painted one or more icons. The oldest surviving icon is that of Christ Pantocrator, dating to the 6th century and found at St. Catherine's Monastery at Sinai. Certainly there are many, many more older icons that are now lost.
"Icons", wrote Leontius of Antioch (4th c.), "are opened books to remind us of God". Kallistos Ware writes:
They are one of the means which the Church employs in order to teach the faith. He who lacks learning or leisure to study works of theology has only to enter a church to see unfolded before him on the walls all the mysteries of the Christian religion. If a pagan asks you to show him your faith, said the Iconodules, take him into church and place him before the icons.
1.J. Getcha, The Typicon Decoded (St. Vladimir Seminary Press, 2012), pp.53-54
5.The Orthodox Church, p.201