In-form opener Kraigg Brathwaite (63) and Leon Johnson (66) put on 143 for the first wicket at the Beausejour Stadium in St Lucia on Saturday.
Bangladesh, who suffered a 10-wicket loss in the first Test, were left to lament a slow start after putting the hosts in to bat.
They dropped two catches as Darren Bravo (44) and Shivnarine Chanderpaul (34) were unbeaten at stumps on a decent first day for the Windies.
Mahmudullah (1-25), Shafiul Islam (1-37) and Taijul Islam (1-79) all took wickets.
Bangladesh opted to bowl first on a green wicket, but failed to make the most of it early on.
Debutant Johnson, who replaced Chris Gayle, and Brathwaite were able to leave plenty of deliveries to reach 61-0 at lunch in the Windies' 500th Test.
Johnson brought up the 100 in style, smashing Taijul Islam for six straight down the ground.
He edged one through slips before Bangladesh finally made a breakthrough as Brathwaite played an awful shot to scoop a Shafiul Islam delivery to Taijul Islam at point.
Johnson fell soon after, trapped in front by a Taijul Islam ball that appeared to be spinning down leg, only to be denied a review for taking too long.
Kirk Edwards was dropped on five but only added another 11 before he hit a Mahmudullah delivery straight to Shamsur Rahman at cover.
While Edwards was unable to make Bangladesh pay, Chanderpaul might on day two after he was dropped on four.