Bangladesh took the lead in the 18th minute but Bahrain soon equalised at the Shas Ul Huda Stadium in Jessore on Sunday.
Having squandered a chance early in the match, Rubel Miah essayed a defence splitting pass to Yusuf Sifat who dribbled away from the goalkeeper before scoring.
Sifat received a caution when he took off his jersey to celebrate his goal.
Jasim Al Shaikh, however, equalised for Bahrain five minutes later following a defensive blunder.
The defenders blocked a shot but failed to clear the ball as Jasim latched on and fired past the goalkeeper.
Sanchez Moreno's men continued to press forward in the second half. Aminur Rahman Sajib and Sifat could not score with only the keeper to beat in the second half.
Bahrain suffered a setback towards the end of the match when Anwar Ali received a second yellow card for a deliberate handball.
With their opponents reduced to 10 men, Bangladesh surged forward in hope but failed to find the winner.
They will take on the Maldives in their second tie of the Group B at the Bangabandhu National Stadium on Wednesday.