We haven’t used the Bible exclusively, but I do think our family scripture reading time helps when the children are learning to read. Each person in the family reads at least one verse each night. As soon as each child is able to talk, we have them repeat after a parent, phrase by phrase, while pointing to the words. We have found that as they learn to read, they quickly enjoy taking over reading words that they recognize during their turn. I’ve been amazed at some of the ‘big’ words my children read when they were just beginning, because they saw them frequently in scripture.
I haven’t done it, but I would think it would be simple to use the Bible as the text when using a CM reading approach. See here: http://simplycharlottemason.com/series/teaching-reading/ Instead of using poems or nursery rhymes, you could just use Bible verses.