https://taronga.org.au/sydney-zoo/getting-here
The 100 Bus (Mosman to City) operates between Mosman (Taronga Zoo Sydney) and the Queen Victoria Building in the city from early morning until around midnight, seven days a week. Buses will run every 10 minutes across the day and at least every 20 minutes in the early morning and late at night.
The 238 bus route travels between Balmoral Beach, the Taronga Zoo Sydney main entrance and the Taronga ferry wharf on the water's edge for passengers arriving or leaving by ferry