Bangladesh could not have had a better start to the day as openers Najmul Hossain Shanto
64(143) and Zakir Hasan 55(109) remained unbeaten at the end of the first session.
Litton Das looked fluent in his brief stay before tea as he played some eye-pleasing strokes and guided Bangladesh to 37/2 at the end of the second session on day two.
The 24-year-old Zakir was selected for the 17-person team after scoring 173 runs for Bangladesh A in the opening four-day match against India A in Cox's Bazar last week.