Like almost everything else pertaining to Mormonism, this is a complicated question with a bottom line answer of, "It depends on what you mean by the terms Mormon and Bible."
The Utah Mormons (who commonly call themselves "LDS" and are by far the largest Mormon sect) believe in three bibles that supplement and in many cases supplant the Holy Bible. In descending order of their deemed importance they are: Doctrine and Covenants, the Pearl of Great Price and the Book of Mormon. It would not be unreasonable to add their Temple Ceremony and numerous prophetic utterances to their list of sacred scripture.
The Utah Mormons also claim to use the King James Version of the Holy Bible. The Missouri Mormons (formerly RLDS, who now call themselves the Community of Christ) use the Joseph Smith translation (JST) of the bible. The JST contains hundreds of changes made to scripture by Joseph under the supposed influence of the Holy Spirit -- Smith had no additional scriptural text and was too poorly educated to challenge the interpretation of the original documents made by scholars of his day (not that it would have mattered ... the KJV is almost universally recognized as an excellent translation).
The Utah Mormons are not really able to explain why they reject such a fundamental text as the JST by their self-proclaimed prophet. The Missouri Mormons are not really able to explain why they reject portions of the Pearl of Great Price and Temple Ceremony. Neither sect can adequately explain why they have significantly different versions of Doctrine and Covenants and the Book of Mormon other than assert that the other sect is wrong.
Other Mormon sects have even more "Bibles." For example, the Wisconsin Mormons rely on the Law of the Lord, a document purportedly translated from golden plates by their prophet King James Strang using Urim and Thummum. A copy of this text is available online.
Hope this helps.
I'm sorry for the oversight.