http://www.sydneybuses.info/travelling-with-us/travelling-with-pets/travelling-with-animals.htm
Pets on Sydney Buses
Customers may also board a bus with a pet such as a dog, cat, bird or other animal. Any such pet must be restrained in a suitable box, basket or other container to be allowed on board as required by the law (NSW Passenger Transport Act and Regulations). The bus driver may refuse to allow a pet on a bus if this poses a risk to the safety of other passengers or the bus. Pets that are not clean, appear vicious, or likely to annoy, threaten or inconvenience other passengers will not be allowed on a bus.