The relationship between a dragon and its rider is an exclusive one. In order to ride a dragon, a dragonrider must connect with it in some way. Nettles did this by bringing Sheepstealer a sheep to eat each day. However, no one could successfully bond with either of the other wild dragons, Grey Ghost or the Cannibal.
Additionally, a dragon will not let anyone ride them except the dragonrider they’re bonded with unless their rider is also on their back. As such, a dragonrider can bring a passenger on the dragon but cannot leave that person up there alone for fear of the dragon violently rejecting them. However, if a dragon’s rider dies, the dragon can form an attachment with a new person. Several dragons have bonded with various Targaryens, as dragons live far longer than humans. Balerion, the great dragon whom Aegon the Conqueror used to conquer Westeros, had four different riders before his death, including Aegon’s son.
Similarly, a dragonrider never rides a dragon if they do not share a bond. This explains why Daenerys only ever rides Drogon, but neither Viserion nor Rhaegal, in “Game of Thrones.” In theory, a rider could bond with a new dragon if theirs dies, but there is no record of it happening. The link between a dragonrider and dragon is so important to the Targaryens that they would place unhatched dragon eggs in the cradles with their babies to encourage an attachment.
