Can a beneficiary have access to the deceased owner of a bank account with a will and a death certificate?

First, you should call or visit the bank to determine the bank's policy in such matters and also find out whether you are named on the account as the beneficiary. If the account was to be payable on death to you then you shouldn't have a problem. If you were not named in the records of the bank and a considerable amount of money is involved the bank may require that you file the will in probate and petition to be appointed the executor. Once appointed the court will issue Letters Testamentary in your name and the letters will give you the legal authority to close that account. The court may also have a speedier process for small estates.