There are no direct bus services between Adelaide and Darwin. Consider rail if you are interested in a none stop overland journey. If travelling by bus consider breaking the journey at least once. A bus journey without break would take a total of 47 hours with a 4 hour wait in Alice Springs. Depart on the Alice Springs bus at 1800 daily.
There are 2 direct train services weekly from Adelaide to Darwin departing at 1220 on Sunday and Wednesday. The trains arrive in Darwin 2 days later at 1730 with a total journey time of around 53 hours (with 4 hour stops to explore Alice Springs and Katherine). Fares start from $363 for students and holders of YHA or backpacker cards. For a bed starting price is $877.