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The anti-gravity motorbike was a vehicle used in the Anti-Grav Olympics by the Doctor. After using it he put it in his TARDIS's garage. The Eleventh Doctor hacked into a Spoonhead which used the motorbike to fly up the side of the Shard in London. (TV: The Bells of Saint John)
It appeared to be a modified Triumph Scrambler from 2013. Who it was modified by is unknown, but knowing his way of making Earth technology "more alien", then it would be safe to assume that it was by the Doctor at some point.