My mother died 2 months ago.and did not have a will . I have a death certifcate showiing I am the only child.. How can i get bank account funds.

You might be able to get the bank account funds, but you would have to be the only heir and all property of your mother, including the bank account, would have to be less than $150,000.  If your mother had a house or other real property, then you would need some type of probate proceeding to transfer the real estate.  Contact an attorney for a full consultation.