I suspect that His Majesty King Geoge III and The Admiralty were the biggest losers. This was a formal expedition.
The motivator behind the fateful trip that resulted in the 'Mutiny on the Bounty' was Sir Joseph Banks, a naturalist appointed by the King as adviser to the Royal Botanic Gardens, Kew. (Two of Kew's gardeners were among the crew.)
Banks urged the King to introduce breadfruit to the West Indies where it could be planted and grown as a cheap food for the slaves that worked on the sugar plantations, and it was Banks who suggested Bligh as the expedition leader. The King in turn ordered the Admiralty to organise the trip. Bligh had collected 1015 plants for the run to Jamaica when things went awry.
Ironically a later breadfruit expedition was carried out by the British Admiralty between 1791 and 1793, but when the fruit evenutally was given to slaves in Jamaica they refused to eat it! There is a good biog of Banks at
http://www.slnsw.gov.au/Banks/
which is part of a fascinating online collection of his archive.