Father passed away leaving an incapacitated step-mom behind; how do I get access to their bank account to pay their bills?

Please go the attorney to discuss this matter as there may be many variations depending on the specifics of the case.

For example, if your stepmom is mentally OK, then she can just put you on the bank account as a joint account holder. Another option - to create a trust and put you in charge as a Trustee. If your stepmom is mentally incompetent, you would need to establish a conservatorship for her (and deal with the property as the conservator). Also, if your father's estate is large, there might be a need to go through probate (and in this case, you'll have access to the property as the estate administrator).