Subject: [State the reasons of this application briefly]
Dear [Designation and Name of Recipient],
First Paragraph: In the first paragraph, you have to state why you need the bank statement and when. Your reason should be a valid one for the authority of the bank to give you a detailed statement.
Second Paragraph: You need to mention the type of account you are currently holding and whether it is a joint account or not.
Third Paragraph: Here, you have to request the bank manager to grant you the statement as early as possible. This is the last paragraph so you have to sum up the letter before signing off. Make sure to be polite and show gratuity as you sign off.