On the Buses Wiki

Tibbles making his Debut in Gardening Time

Tibbles is a White Persian cat who belongs to Jack Harper.He is possibly the second cat he owns as he was previously shown with another cat in The Cistern.

It is not known where Tibbles came from but it is most likely that he came from a Pet Shop possibly since the first cat he had died and he got Tibbles to replace him. Tibbles only appearance has been in Gardening Time when Jack used him to destroy Blakey's flowers (who now lives next door since Stan's departure) he later was sleeping in Jack's bedroom with Jack when he told him to stop snoring until he discovered it was Blakey cutting his tree down.