You need to consult a probate and or trusts and estates attorney in your county. Did she have a will? Were you a co-signer on the account? We don't have enough information to provide an answer. Generally, if she died without a will, your state's intestate succession laws would dictate who gets the money. If she had a will, that would dictate who gets it unless the bank account is a joint account. You need legal advice as to her other assets as well. Good luck.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
First, please accept my condolences on your loss. WA has a "short form" probate that is appropriate when there is no real property in the estate and the value of the other estate property is minimal. You can get a certified copy of her death certificate from the Health Department and you take that to the Clerk of the Superior Court,file an affidavit regarding the value you know about her property,and that there is no real property (if that's the case) and the Clerk will issue you letters testamentary. You take that to the bank. If she owns real property you have to probate it formally.
There are lots of skilled probate attorneys in Tacoma who can help you with this. Hope this helps you - Elizabeth Powell