If your mom had a trust and the bank account was properly transferred to be owned by the trust, then the trust should be able to distribute it. The bank should not give you any problems.
If the bank account was not owned by the trust, but the amount in the account plus the total value of any other assets she owned outside of the trust with no beneficiaries adds up to less than $100,000, then you may complete a Small Estate Affidavit. A Small Estate Affidavit must be properly filled out and submit that along with a death certificate and a copy of her will to the bank and the bank must disburse the funds without a probate case having been opened.
If the bank account and the other assets total is more than $100,000 than you will have to open up a probate case in the county court of which your mom resided. Either way, I would suggest you contact a probate attorney to assist you with completing the Small Estate Affidavit or to open a probate case in the county court.