Finch, Warner and Labuschagne struck fifties to give Australia a fighting total.
England Test series in Sri Lanka postponed due to coronavirus.
The 13th season of the marquee T20 tournament, was originally scheduled to begin on March 29.
The first match of the T20I series between India and South Africa had also been rained off, at the same venue.
Before home series Bangladesh will travel to Ireland on May 8 to play three ODIs and four T20Is.
BCB has postponed the two international T20 matches between Asia XI and World XI in light of the current COVID-19 outbreak.
Liton Das heroics help Tigers outclass visitors in second T20I to complete clean sweep.
A stunning last over blitz from Rashid Khan tied the game, before Joshua Little bowled a top Super Over conceding only 8 runs
Soumya Sarkar fires Bangladesh to thumping win against Zimbabwe
Rohit Sharma, who sustained a calf injury last month, does not feature in the squad.