Marsh was unable to feature in the series opener as he continued his recovery from an ankle injury, leaving wicketkeeper-batter Josh Inglis to lead the side in Mirpur.
However, the stand-in captain could not prevent Australia from slipping to an 86-run DLS defeat, as Bangladesh claimed only their second-ever ODI win over the six-time world champions.
The loss left Australia trailing 1-0 in the three-match series and increased the importance of Marsh's return to the squad.
Australia's urgency to bounce back was evident ahead of the second ODI. Despite having a scheduled rest day, several players attempted to train at the Sher-e-Bangla National Cricket Stadium on Wednesday. Their plans, however, were disrupted by rain.
Prior to the tour, Cricket Australia had indicated that Marsh would remain in Perth for further medical assessment and rehabilitation, with no certainty over his availability for the Bangladesh series. Australian media later confirmed that the all-rounder would miss the opening ODI.
Now that Marsh has joined the squad in Dhaka, Australia will hope the experienced all-rounder can help revive their campaign and keep the series alive in the remaining matches.