By plane
While Bendigo does have a small airport, it will likely be much more convenient to fly into Melbourne. From there, hire a car and take the M79 Calder Freeway which starts just by the airport. If you do not wish to drive, take the Skybus into Southern Cross Station and get the train to Bendigo. Alternatively take the shuttle (http://www.bendigoairport...) direct to Bendigo from the airport.
By train
Bendigo is served by trains which run from Melbourne's Southern Cross Station into the south of Bendigo. These usually run about once an hour. The journey takes approximately two hours from Melbourne. As the route is used by many commuters trains may be more crowded in the early morning and late afternoon/early evening on week days. From the station, most of the CBD is within walking distance. Alternatively buses run into the centre of the city and other parts of Bendigo from the station. In addition to the main station, the trains also often stop at the outer Bendigo station of Kangaroo flat. It is unlikely to be a better option than the main station due to having less connecting public transport and little of interest in that area.
Vline also operates a coach twice daily from Adelaide direct to Bendigo.
By car
Bendigo is just over one and half hours drive north of Melbourne on the Calder Freeway Highway. The freeway is now all dual carriageway. The final stretch of the Calder duplication project opened to traffic on 20th April 2009.
If you are coming from Sydney, take the Shepparton exit from the Hume Freeway, and then follow the signs from Shepparton to Bendigo.