There’s one person to look out for when looking for Bengali resources for English speakers: Hanne-Ruth Thompson. All of the resources on this page were created by her.

Books

• Beginner’s Bengali (Bangla) with Online Audio. You can find the audio on this page.

• There are two dictionaries, Bengali (Bangla)-English/English-Bengali (Bangla) Practical Dictionary and Bengali (Bangla)-English/English-Bengali (Bangla) Dictionary & Phrasebook, though for the latter phrasebook, do read the review by “xmanforever” and decide whether it suits you.
  
• There is a comprehensive grammar of 800 or so pages.