Charlotte Edwards top scored with 60 runs in 51 balls smashing seven fours while Natalie Sciver emerged as the other top scorer with a 22-ball-27-run effort.
Bangladesh's Jahanara Alam claimed three wickets conceding 32 runs in four overs.
Nigar Sultana's knock of 35 runs in 28 balls with four fours and a six was the highest individual score for Bangladesh while Salma Khatun remained unbeaten at 32 in 30 balls with four fours.
England's Anya Shrubsole took two wickets in four overs conceding 27 runs while Katherine Brunt, Jenny Gunn and Danielle Hazell also helped themselves with a wicket each.
Edwards was adjudged the player of the match.
Brief scores: England 153/7 in 20 overs (Charlotte Edwards 60, Natalie Sciver 27; Jahanara Alam 3/32, Salma Khatun 1/28) won against Bangladesh 117/6 in 20 overs (Nigar Sultana 35, Salma Khatun 32; Anya Shrubsole 2/27, Katherine Brunt 1/17).