Outside of Utah, it is not uncommon to hear the Book of Mormon being referred to as the Mormon Bible. This statement is usually made by a person ignorant of how many scriptures the people who follow the Mormon faith actually use. The Mormon Bible is nothing more than the King James Version of the Bible used by many Protestant denominations. Joseph Smith, Jr. did work on a translation of the Bible before his death in the 1840s, but the Community of Christ, formerly the Reorganized Church of Jesus Christ of Latter Day Saints, holds the copyrights to the Joseph Smith translation.
Calling the Book of Mormon the Mormon Bible is inaccurate. The complete canon that makes up official Mormon doctrine is The King James Version of the Bible, the Book of Mormon, the Doctrine and Covenants, and the Pearl of Great Price. If the set of Mormon scriptures you own is published by Deseret books, chances are the Joseph Smith translation of the Bible will be referenced in the footnotes of the Deseret books printing of the standard King James Version.
The Book of Mormon, referred to by many non-Mormons as the Mormon bible is simply a companion scripture to the Bible thethat tells the tales of people living in the ancient Americas. The Book of Mormon follows two groups of people who came over from the old world, both of which were eventually wiped out in wars. The first which came to the New World after the Tower of Babble and the second before the destruction of Jerusalem.
The Doctrine and Covenants is a series of revelations received by the Mormon founder to give instruction and guidance to members of the church. The Pearl of Great Price, the shortest book of Mormon scripture supposedly contains translations of Egyptian scrolls bought by the prophet. The legitimacy of the translation was brought into question in a book call Egyptian scrolls bought by the prophet Joseph Smith. Despite these also being works of scripture used by the Church of Jesus Christ of Latter Day Saints, they are not viewed as an additional Mormon Bible.
The legitimacy of the translation of the Book of Abraham was brought into question in a book called By His Own Hand Upon Papyrus by Charles M. Larson. Egyptologists have long thought the facsimiles were in fact common funerary texts and the book expands upon this argument.
The Mormon Bible, as many people understand it is just another book of Mormon scripture that serves as a companion to the bible. Those who continu,e to refer to it as the Mormon Bible should go to the official Mormon website and find out for themself what comprises holy writ for member of the Church of Jesus Christ of Latter Day Saints.