Desiring the opportunity to interview in person for an Bank Manager position with your Institution, I thank you in advance for your time and consideration.
I am pleased to present my resume to you for consideration as an (bank manager, bank branch manager, whatever applies) at the (name the branch) of (Name the bank). I possess a (type of relevant degree) from (name of university). Having the desire to provide both informative and quality customer service to all bank customers, I am certain that I will be a valuable asset to your institution.
As my resume will demonstrate, my educational training (and work experience if applicable) has been geared toward providing competent financial counsel to customers as well as motivating employees to provide a pleasant experience as well. Throughout my formal training, I have been given ample opportunities to prepare to (gear it to the job), As a result, I feel genuinely prepared to further the goals of your company in a professional, courteous and complete manner.
My greatest strengths include a desire to help those in need of financial advise as well as making customers feel at home so that they will return when services which make a bank profitable are needed. Actively engaging in (any activity that makes you stand out. ie serving as a certified financial adviser, experienced in loan applications and processing, whatever applies)
I am confident that I will be an asset to (name the bank). I look forward to meeting with you to discuss your institutions goals and how I can help you achieve them as a (whatever the actual position is that you are applying for). Thank you.
This is a basic layout of a cover letter for bank manager positions. You can adapt it and put it into your own words. I just wanted to give you an idea of what a cover letter for banker and bank branch managers should look like