Crosby started his career in 1976 as a market analyst with Golden Fleece Petroleum. He then moved into politics as a research assistant in 1978 for Senator Baden Teague. In 1980 Crosby became executive assistant to the Harold Allison, then Minister of Education and Aboriginal Affairs. Crosby became executive assistant to Martin Cameron in 1992, then Leader of the Opposition in the South Australian Legislative Council. Between 1986 and 1991 Crosby held a number of corporate affairs positions in the Australian private sector.