There are services daily between the city and Adelaide Airport. The JETBUS (J1, J2) service is operated by Adelaide Metro and you can pay the ticket fare with your credit card, an Adelaide Metrocard, but not cash.
To Adelaide Airport
The airport JETBUS service operates from 4.39am each morning Monday to Sunday including Public Holidays to Adelaide airport from X1 bus stop on Currie Street. The first service each day arrives at the airport at 4.57am, which is more than enough time for the first domestic flight that depart from 6.00am. The last service to the airport each evening is at approximately 10.53pm.
To Adelaide City
The JETBUS service from Adelaide airport leaves from 5.01am each morning Monday to Sunday including Public Holidays to the city. The last service from the airport departs at 11.34pm Monday to Sunday including Public Holidays.
When boarding the bus head into the city and get off near Light Square on Currie Street at bus stop C1, from where you cross the road and walk up 5 minutes to Sunny’s, which is on the corner of Morphett St & Franklin St.
These links will give you all the info on timetables and planning your trip:
Ticketing
Between 9am to 3pm Monday to Friday, all day Sunday, and public holidays is ticketed at the off-peak rate. All other times is at the peak rate.
Follow this link for Adelaide Metro Fares