This was never addressed in the final version of the film, but the book had Landon ask her the same question. The Bible that she carried belonged to her mother. (I had guessed as much, but the book confirmed it).
An interesting note about this. If you recall, when Jamie gives him the book of quotations that had belonged to her mother, she told him “don’t worry, it’s not a Bible.” In the book version she DID give him a Bible for Christmas, in fact, it was HER Bible!