I would recommend the book The Armed Transport Bounty, by John McKay. It was published by Conway Maritime Press Ltd in 1989 as part of their Anatomy of the Ship series. You should be able to get a copy via a second-hand dealer as I believe it is no longer in print.
Knowing how thorough John McKay is in his research I would say this is probably the definitive work on the design, construction and rig of the Bounty (the book is profusely illustrated with detailed line illustrations, accompanied by an authoritative text and a number of reproductions of photographs of the replica, built for the film).
Good luck with your build! I look forward to seeing photos of your Bounty!