I’m sorry to say that it is not a myth. But it is greatly misunderstood.
There were places and times where the Church put the Holy Bible on the list of forbidden books. The bans were always localized to specific places and always temporary.
There was one place, I believe it was somewhere in France (working from memory here), where heretics were teaching that physical creation was evil and the spirit was good. These heretics were using the Bible to teach this heresy and were using Sacred Scripture to encourage people to commit suicide. The church rightly clamped down and the ban was lifted when the controversy subsided.
There was another occasion some time in the middle ages, where people were using the Bible to teach that all oaths were evil. The feudal society of that time was based on oaths. Oaths of allegiance were what held communities together under a ruler who provided protection for his subjects. People started renouncing their oaths of alliegiance and it led to riots and food shortages. In order to quiet the social unrest caused by those who were interpreting scripture incorrectly and teaching error, the Church made an effort to stop public use of Bibles. Once order was restored, the ban was lifted. The ban was an act of mercy for a suffering population.
The “Myth” that the Church chained Bibles so that no one could read them gets similar treatment from both sides. Non-Catholics hear that the Church chained Bibles so that no one could read them and it sounds provocative. Catholics say it never happened. But it did happen. That the Church chained Bibles is not a myth. The Church absolutely chained Bibles, but they did it for the same reason the post office chains the pens to the table - so that they don’t get stolen! Bibles were hand copied, and very valuable, and no one could read a Bible if it was stolen so the Church chained them to the table just like the post office chains pens; not to prevent people from using them but so that everyone can use them.
And burning Bibles too. No myth there. In fact Protestant Churches have burned Bibles. There was a Bible published in 1795 which today is known as the “Child killer” Bible.
***But Jesus said unto her, Let the children first be filled: for it is not meet to take the children’s bread, and to cast it unto the dogs. ***(Mark 7:27)
The Child Killer bible has a typo, so that it read, “Let the children first be killed” instead of “first be filled.” Some guy who read it went out and killed his children.

These Bibles were rounded up and destroyed.
My favorite is the Vexing Wives Bible from 1638 - In a KJV Bible at Numbers 25:18 it reads “for they vex you with their wives” instead of “with their wiles.” I personally think that was divine inspiration.
You can have a laugh at some of these Bibles at the Bible Collector Society website
curiosities page.
My point is that the church did discourage reading the Bible from time to time and in certain places, the Church did chain Bibles and Bibles were burned. But that isn’t the whole story.
-Tim-