In the last section of Part One of Verbum Domini, the Holy Father states that "authentic biblical hermeneutics can only be had within the faith of the Church". The paradigm - the model - of this is Mary's fiat: "May it be done to me according to your word" (Luke 1:38). Mary demonstrated faithful obedience to the angel's message. We're to show similar faithful obedience to the Church in our reading of Scripture.
Is this too restrictive? No. The foul lines don't restrict me from playing basketball; they allow me to play. The lines on the road don't restrict me from driving; they allow me to enjoy the freedom of the road. The limits give the freedom. This seems paradoxical to us only because we, as a culture, have a lousy working definition of freedom.
In the same vein, "the ecclesial context" is not a rule applied to Biblical study but an intrinsic part of it, as the lines are part of the road or the playing field. This context - reading the Bible within the Church - allows us to enjoy fruitful Bible study. "(T)he ecclesial context...is something demanded by the very nature of the Scriptures and the way they gradually came into being."
Reading the Bible without communion, without a full faith life, "might suggest interesting elements on the level of textual structure and form" but could not begin to plumb the depths of the meaning of God's written Word.
What does this mean for us? If you want rich Scriptural study, live a rich Catholic life. The Mass is Scriptural. The Catholic life is Scriptural. The more we live it, the more we'll see it in Scripture, and when we recognize ourselves on the surface of Scripture, we'll be more ready and able to dive past that reflection and into the ocean of His Word.