The dodo femur was part of a sale called Out Of The Ordinary held by Sworders Fine Art Auctioneers.
It had been expected to fetch between £2,000 and £3,000 but went under the hammer for £3,800 on Tuesday.
The buyer has not been revealed, but there is a ban on exporting dodo bones from the UK.
An spokesman for Sworders Fine Art Auctioneers said: “The story of the dodo is particularly important as it demonstrates one of the first occasions that man realised that human actions alone caused a species to die out.”
The dodo came to greater public prominence after one appeared in Lewis Carroll’s Alice In Wonderland.
It was related to the pigeon family and lived solely on the island of Mauritius in the Indian Ocean, east of Madagascar.
The flightless bird had no natural predators, and adapted to living life on the ground until the Dutch colonised the island, starting in the 16th Century.
At this point dodos became hunted for sport.
Colonisation also brought new species to the island, such as rats, dogs, cats and pigs, which all contributed to the dodo’s decline of the bird and it died out in the 1680s.