The story of the Bounty has always fascinated me, and I've read many books on the subject. If you want to read a factual account of the mutiny and aftermath, try:
• The Bounty, by Richard Hough - (Originally published as Captain Bligh and Mr. Christian) An excellent historical account. I have one major complaint. Hough comes to the conclusion that the troubles between Bligh and Christian were due to a homosexual relationship gone bad. This is just Hough's "interpretation." There are no facts to support it.
• Mr. Bligh's Bad Language, by Greg Dening - An odd book that wanders all around the place, but is always interesting. It goes into Captain Cook's murder on Hawaii, Polynesian customs, all sorts of things.
• The Mutiny of the Bounty, by Sir John Barrow - Originally published in 1831, but available in libraries in a recent edition. Barrow was the Permanent Secretary to the Admiralty in the early 1800s. His book includes the voyage, the stay on Tahiti, Bligh's voyage, Pandora's voyage, the court-martial and the fate of the mutineers. Very interesting.
• A Book of the Bounty, by George Mackaness (ed.) - This is an old Everyman's Library edition, last published in 1952. Good luck finding it, but it's worth the effort. It contains Bligh's narrative of the mutiny, the actual report of the court-martial and an appendix by Edward Christian, Fletcher's brother, blaming Bligh for the mutiny, Bligh's reply to Edward and various other letters relative to the Bounty.