Bandit seems to be completely terrified of all dragons, except maybe Moonwatcher, as she saved him from being eaten. Bandit was nearly captured and killed by dragonets in the prey center when he escaped from his cage, Qibli having opened it to get a better look at him. He was also hungry enough to allow Kinkajou to feed him fruit, but Moon later convinces Winter to feed him cooked meat. Bandit appears to be lonely. Moonwatcher can't fully read what he is thinking since he isn't a dragon, but she can understand his feelings (a phenomenon also observed by Listener in Darkstalker (Legends)). Winter sets Bandit free at the end of Moon Rising, mainly because he would freeze to death in the Ice Kingdom. At first, Bandit seems to not want to leave, maybe because a big menacing dragon was standing near the exit, but after a bit of yelling coming from his owner, Winter, he scurried off into the forest.
In Winter Turning, in the beginning of the book the end of Moon Rising in Winter's point of view. Winter is trying make Bandit leave because there would be no way that Bandit would be able to survive in the IceWing kingdom.
In Escaping Peril, Peril notices a pack of scavengers in the desert near Possibility and one was sitting separate from the other ones, looking sad. It is possible that this was Bandit, as he was described to have brown fur on his head by Moon.