The victory at the Changlimithang Stadium in Thimphu on Wednesday extended Bangladesh’s dominant run against their South Asian neighbours.
Bangladesh were in control of the match from the beginning and took the lead in the 20th minute when Shaheda Akter rifled her shot home.
Rosina Akter doubled the lead in the 31st minute.
Bangladesh will play their second match on Friday against Nepal, who started the tournament with a 4-1 defeat to defending Champions India in the other match on Wednesday.
On their way to win the first edition of the tournament in 2017, Bangladesh beat Bhutan 3-0.
In the next edition in 2018, Bhutan conceded a 5-0 defeat to runners-up Bangladesh in the league stages.