Greetings of the Feast:
You are quite right. The texts of the liturgical services are saturated with Scripture. What is not a direct quotation is usually a composition based on a specific scriptural reference, as in the troparia of canons, sessional hymns and the like. Having "mused" a bit more thoughtfully, one only need look to "The Way of the Pilgrim" to discover the centrality of the Bible in the lives of pious Orthodox Christians. The very first chapter describes how attentively the pilgrim listened to the readings in church, and how he then ran to his Bible to look up the reading for himself. In fact, his copies of the Bible and of the Dobrotoljubije [Philokalia] were his only possessions. Later in the text, there is a section where he refers to a traveling companion, whose custom it was to read the holy Gospels through every evening.
And even though a complete Bible in Church Slavonic was not printed until the 17th century, the Psalter [which, as St. Athanasius says in his Letter to Marcellinus
, is a recapitulation of all the other books in the Old Testament] and Gospels were always widely available. I don't doubt that many pious Christians and monastics could recite the Psalter by heart, and an examination of any Church Slavonic psalter confirms that reading the Psalter on behalf of the departed, and as part of one's prayer rule, was [and is] a very important practice in Russian Orthodoxy.
A slight digression, if I may:
The answer to this, David, is simple. There is so much biblical content in the liturgical services (including in the prayers, canons, stikhera, troparia, kontakia, etc, as well as the "formal" scripture readings such as psalms, OT and NT readings), that an ordinary Christian (literate or not) who attends Vespers, Matins and Liturgy frequently and is attentive, will soon become familiar with scripture and its teachings.