The context for my answer is the later medieval Latin west.

Movable type is invented in 1450s Germany because that is the first time and place in medieval Europe where it was economically viable. That is, it was the first time books could be produced and expect a market existed to buy them, rather than scribes copying out a single text on demand. (In the decades prior, yes, we see some efforts at 'commerical' book production by hand.)

I start with this to set the context: for most of the Middle Ages, books were extremely rare, period. They were insanely expensive to produce in terms of material and labor, and literacy rates were single digits-low. There was no particular prejudice against the Bible in this respect. In fact, while "the Bible" did not really exist as a single book due to the time of copying out 626982 words and the cost of the parchment to hold them, individual Psalters were somewhat common among the lay nobility as the basic prayer book of the Middle Ages. (And if not a full Psalter, then a Book of Hours filled with...psalms.)

From 1300, urbanization and a growing urban gentry, cheaper book materials (paper!), and the demands of a burgeoning economy led to increasing literacy rates among the urban middle classes and elite. In the 14th and early 15th century, we still see very few full Bibles. However, biblically derived material, which Brian Murdoch has termed the "medieval popular Bible," was in heavy demand among the literate.

Gospel harmonies, for example, were the medieval equivalent of the modern Bible storybook, knitting the four Gospels into a narrative of Jesus' life and Passion. Pericopes broke up the Gospels or the epistles into the Sunday and feast day liturgical readings, sometimes with commentary. Although they were originally intended as aids for pastors writing sermons, lay people owned these and, we know from marginal notes, brought them to church to follow along with the readings! And stories from the Bible gained "fanfiction" of sorts: extended legends of Adam and Eve, Susanna (especially popular among English women), Mary Magdalene available in countless Latin and vernacular editions alike.

When lay people copied their own vernacular prayer books in German and Dutch cities (in England and France, they were mostly using Latin Books of Hours), they frequently included passages or verses from the Bible, in their vernacular. When they read catechetical texts by clerics, those authors had no qualms about including biblical verses right alongside their original writing or quotes from Augustine. In England, the Latin versus vernacular situation was a bit tetchier thanks to anxiety over Wyclif and the Lollards in particular (but not exclusively). So the poem Piers Plowman, for example, switches from English to Latin when it verse-checks the Bible. Italian authors had no such fears.

And the growing mania for the Bible in the 15th century was not restricted to physical texts. Sermons were a major public event, of course. While the biblical readings themselves might sometimes still be in Latin (although, we think, sometimes immediately followed by a vernacular translation), the explanation of the passage and its application to the moral life of listeners would have been in the vernacular.

But beyond the world of sermons, public singing performances and civic/guild dramas were also important avenues of public exposure to the "medieval popular Bible," particularly in narrative form.

The invention of movable type only heightened this demand. From 1466 to 1487, nearly 30 complete vernacular Bible editions were printed in Germany alone. People demanded access to the Bible, and they got it.

It's no accident, indeed, that Das wort gottes! became the rallying cry of the Reformation. At a time when popular religious sentiment fundamentally changed the course of history, what people demanded, above all, was more and better access to the Bible--through sermons especially, but also through new and better translations. Luther holed up in the Wartburg wasn't alone. Humanists in Rotterdam, in Florence, in Paris were re-translating and re-editing the Bible so the texts they worked from and wrote from and preached from would be the truest possible ones.

Based on the evidence, I think it's fair to say that increasing access to biblical material in late medieval Europe mostly made people want more of it.