There is no central repository for bible records, but numerous organizations have collections of them. Two that come to mind are the DAR Library and the Virginia State Library.
You might try the Kentucky State Library (I assume there is one), State historical society, a county historical society or genealogical society.
I did a google search for “collection of bible records” and got lots of hits. I only looked at the top few hits, and Kentucky was not there, but still could be on the list somewhere. A more focused search might be more fruitful.