Bashar, who lost his captaincy after making just 46 in four Test innings against India at home last month, scored 60 not out to help his team reach 183-5 at stumps on the opening day of a three-day match against Sri Lanka 'A'.
Bangladesh were struggling at 73-3 after electing to bat, but Bashar steadied the innings with a 75-run stand for the fourth wicket with new captain Mohammad Ashraful (37).
Opener Javed Omar (34) and Rajin Saleh (21) were the other main scorers.
Left-arm spinner Rangana Herath, who has played 12 Tests for Sri Lanka, was the most impressive bowler with 3-51 off 20 overs.
Bangladesh will play three Tests and as many one-day internationals on their current tour of Sri Lanka. The first Test begins here on June 25.
Bangladesh 1st innings 183-5 (Habibul Bashar 60 not out, Mohammad Ashraful 37, Javed Omar 34, Rajin Saleh 21; Rangana Herath 3-51) v Sri Lanka 'A'.