A. Melvin McDonald discusses the use of "Bible" in the Book of Mormon; argues that the use of "book" in the KJV is a parallel example of a translator's anachronism.
A. Melvin McDonald, The Day of Defense (Sandy, Utah: Sounds of Zion, 1963), 105
You mentioned that the word “Bible” was used around 600 years before it was coined. Did you know that in Job 31:35 we have the quotation, “Oh, what one would hear me! Behold my desire is, that the Almighty would answer me, and that mine adversary had written a book.” The word “book”, placed in the translation as the words of Job, could not have been used as such. The word “book” was not even coined until hundreds of years later. There is no such thing as a book in those days. (See Apology for the Book of Mormon - McGavin.)
What the writers of the King James Version did was to decipher the meaning and place the word “book” into their translation so the readers would know what Job was referring to in his writings.