While there are plenty of bus driving games available for the PC market, tracking down some for PS2 is considerably harder. There is one "pure" bus driving game for PS2, but a few other games feature buses as playable vehicles. While the buses are not the main focus of these games, they can be driven in certain missions.
Tokyo Bus Annai 2 (Tokyo Bus Guide 2)
This game came out in Japan and is available for the "NTSJ/J" PS2 consoles only. With 18 routes to select from for driving during the morning, afternoon and evening, this is one of the more comprehensive bus driving simulations available on PS2. As a bus driver in Tokyo you will have to obey traffic laws, open and close the doors for your passengers and listen to radio communication. Although the game is Japanese, it is not too hard to figure out what to do and serves as a good introduction to the genre. This game was released in 2005.
The Simpsons: Hit & Run
Among the many vehicles to drive in this game, you will be able to use the school bus from "The Simpsons" during mission 4 of level 3 and mission 1 of level 6. This is an arcade game and not a simulation, so don't expect an accurate portrayal of bus driving.
Grand Theft Auto---Vice City
In Grand Theft Auto Vice City for PS2, you will be able to steal any vehicle in the game, including the regular city buses. If you manage to steal a bus without being seen by the cops, you will be able to play bus driver for a while, earning extra cash. Stop at the bus stops and collect £3 from every person getting on the bus.