Here is the link to estimated western European illiteracy rates, from the 1500's on.
https://www1.umassd.edu/ir/resources/laboreducation/literacy.pdf

Latin by 1500 was still the language of the elite, not just some. With the advent pf the press
in the 1450's, publications could be distributed cheaper & faster, an set the stage for increase in literacy, & demand for the vernacular, not versed in Latin. Money did talk in those times to.

Perhaps you can provide a source showing the Church suppressed lay access to the Bible. 

Rather strange comment, since it was the Church provided the means of preserving & producing most of the ancient documents.  Because of the cost of producing a Bible, (100's of animal skins for starters), maybe not everyone could handle one, but their use was not lay restricted. Some Bibles, considered heretical, may have been  restricted, but I believe that was all.