Hagrid’s ride

How did Hagrid travel to the Hut on the Rock? With this passage in OP21, fans guessed that Hagrid might have come to the Hut by riding a thestral:

“… they aren’ unlucky, they’re dead clever an’ useful! Course, this lot don’ get a lot o’ work, it’s mainly jus’ pullin’ the school carriages unless Dumbledore’s takin’ a long journey an’ don’ want ter Apparate …”

However, in DH4 he says “We’ll be on the bike, brooms an’ thestrals can’t take me weight, see.” So how did Hagrid travel to the Hut on the Rock? Did he ride the flying motorcycle? Then where did he leave it?