It was for the first time that Bangladeshi fans had burned effigies of the captain of their national team, although the side had lost 117 one dayers out of 154 since 1986.
Bangladesh, who beat India by five wickets and Bermuda by seven wickets in the group phase, lost to Australia and New Zealand by 10 and nine wickets respectively in their first two matches of the second stage Super Eights.
Students at Dhaka University burned the effigy of Bashar, calling for the skipper to quit.
The burning of effigies of failing cricketers is common in India and Pakistan.
Bashar had been singled out for particular criticism after scoring only 52 runs in the four innings he has had so far in the tournament.
In the last match against New Zealand on Monday, Bashar scored nine off 21 balls before he was run out.
''Bashar is continuously showing us he is losing his indispensable tag in one-day team,'' Aminul Islam, a former skipper wrote in the daily New Age newspaper on Wednesday.
''The stage was set for him to lead by example, but his sluggish running between the wickets cost the team dearly again,'' Aminul wrote.
''Had he managed to stay a few more overs, the tail-enders could have taken Bangladesh easily beyond 220 runs,'' wrote Aminul, who led Bangladesh in their first World Cup in 1999.
The team have won only one Test match, against Zimbabwe in 2005, and conceded 39 defeats since qualifying as a Test-playing nation in 2000.
This time the expectations at home were high as Bangladesh moved to the second round of the World Cup for the first time in their third tournament since 1999.
Bangladesh still face South Africa (Apr 7), England (Apr 11), Ireland (Apr 15) and West Indies (Apr 19).