Catholics never needed to have "permission" from their bishop to read the Bible. Most definitely not within the lifetime of anyone still breathing. This sounds suspiciously like a Boettner-style canard made to sound like a personal anecdote. IF there is truth to it, perhaps you misconstrue the *possible* insistence on the bishp's part that prior permission be obtained by him before one went to read, say, the KJV. Catholics do regard that particular translation with wariness, since it has agenda-driven translation issues and is missing seven books and parts of several others.
On my honor it is true. This occurred sometime in the 1960's. I think it may have been before Vatican II, in fact I'm sure of it because I remember going to some Latin Masses back then and I think the Latin masses were done away with back then.
Now maybe my Catholic friends misunderstood whether they were allowed to read the Bible, but I distinctly remember being shocked that they needed to obtain permission before they were allowed to read it.
Now if you think it is a "Boettner style cannard" then my opinion of the credibility of "Bottner style cannards" has risen dramatically. In that case I would have to assume that a "Bottner style cannard" is as trustworthy as I am.
In centuries past, they did. In fact it was a death penalty offense to possess a non-registered Bible in several European countries.