Australia A were tested for the first time in the tournament, but an unbeaten half-century from Callum Ferguson gave them a four-wicket win and secured their place in the final of the tri-series.
Bangladesh won the toss for the second time in their three-match one-day international series against Australia, but the hosts have chosen to bat first at the Shere Bangla National Stadium.
Mike Hussey and Nathan Hauritz have been ruled out of the World Cup through injury and will be replaced by Callum Ferguson and Jason Krejza respectively.