If you already have bank accounts in good standing, then you will be able to keep those accounts open after you file bankruptcy. However, if you have credit lines, credit cards, or secured loans with those same institutions, then the banks may close your bank accounts if you close those other credit accounts.
You want to have at least one open bank account, in good standing, without any lines of credit attached to it prior to filing bankruptcy. Otherwise, it will be very difficult to open an account after filing bankruptcy.
If you have an account in overdraft, you may be able to keep that account if you pay the balance back up to zero after filing. This is generally not worth it unless your overdraft is very small, like $200 or less.
If you are already have banking issues, you may want to read here instead: