How many times have Bangladesh beaten India in international cricket? 

Bangladesh have beaten India 9 times in international cricket (8 in ODIs and 1 in T20I)

Bangladesh's first-ever win over India was during the second ODI in Dhaka in 2004. BAN won by  15 runs

2nd ODI, Dhaka, 2004

In 2007 ODI World Cup, BAN clinched a famous five-wicket win that would eventually knocked IND out

2007 ODI World Cup, Port of Spain 

Sachin Tendulkar's hundred went in vain as BAN won by five wickets 

2012 Asia Cup, Dhaka 

Bangladesh clinched a 2-1 ODI series win over India at home in the summer of 2015 

2015 ODI series in Bangladesh 

The two teams met again in an ODI series in 2022, which Bangladesh won 2-1 

2022 ODI series in Bangladesh 

At the Asia Cup in 2023, Bangladesh stunned India by six wickets in a Super 4 match in Colombo

2023 Asia Cup

2nd T20I, Rajkot 2019

Bangladesh's only win over India in a T20I so far was in Delhi in 2019, when Mushfiqur Rahim starrred with the bat 

Also see: List of Test matches abandoned without a ball being bowled