"We need to win this game and get our pride back," Bashar said ahead of Friday's match.
Bangladesh and Zimbabwe both have been knocked out of the main tournament after suffering two defeats in as many games against Sri Lanka and defending champions West Indies.
"We came into this tournament to do a lot better and we want to win at least one game," said the Bangladesh captain, whose team lost by 37 runs against Sri Lanka and by 10 wickets against the West Indies.
Zimbabwean coach Kevin Curran said his side held an edge going into their last league match against bottom-placed Bangladesh.
"We need to be on top when we play Bangladesh tomorrow. We beat them 3-2 recently and we have that advantage," Curran said, referring to his team's victory in a home one-day series.
Zimbabwe lost to the West Indies by nine wickets in their opening game and then to Sri Lanka by 144 runs.
The West Indies and Sri Lanka have both qualified for the main draw that features world champions Australia, India, England, South Africa, New Zealand and Pakistan.
Zimbabwe: Prosper Utseya (captain), Gary Brent, Chamu Chibhabha, Elton Chigumbura, Anthony Ireland, Tafadzwa Kamungozi, Hamilton Masakadza, Stuart Matsikenyeri, Tafadzwa Mufambisi, Tawanda Mupariwa, Ed Rainsford, Piet Rinke, Gregory Strydom, Brendan Taylor
Bangladesh: Habibul Bashar (captain), Shahriar Nafees, Khaled Mashud, Mohammad Rafique, Mohammad Ashraful, Mashrafe Mortaza, Rajin Saleh, Abdur Razzak, Aftab Ahmed, Syed Rasel, Shahadat Hossain, Farhad Reja, Saqibul Hasan, Mehrab Hossain
Umpires: Steve Bucknor (WI) and Daryl Harper (AUS)
TV umpire: Simon Taufel (AUS)
Match referee: Ranjan Madugalle (SL)