Opting to bat, England scored 153 for seven with Edwards scoring 60 off 51 balls with seven fours.
Apart from Edwards, Natalie Sciver smashed 27 off 22 balls with two boundaries before the slog overs, and Katherine Brunt and Danielle Wyatt hammered 17 and 15 in eight and seven balls, respectively, helping England reach the 150-mark.
In reply, Bangladesh were never in the hunt as they finished on 117 for six despite 64 run-stand for the fifth wicket between Nigar Sultana (35) and Salma Khatun (32 not out).
Bangladesh started the run chase rather poorly, losing wickets at regular intervals. They were 46 for four in 10.3 overs.
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Sharmin Akter(0), Ayasha Rahman(2), Fargana Hoque (19), were removed by Katherine Brunt, Anya Shrushbole and Danielle Hazell respectively. Rumana Ahmed was unfortunately run out for 19.
Nigar and Salma did show some urgency but it was not enough to win the match.
Earlier, when England batted Sciver put up a crucial 47-run partnership with Edwards for fifth wicket.
However, Edwards kept the board ticking showing a lot of calm. She planned her innings well and paced it to perfection.
Brief Scores: England 153/7 (Charlotte Edwards 60, Natalie Sciver 27, Jahanara Alam 3/32)
Bangladesh 117/6 (Nigar Sultana 35, Salma Khatun 32, Anya Shrubsole 2/27).