Hi all,
Sorry for the late response on this but my fiancée did call the bank and they said I would need a California Driving License or California ID Card and just the membership application form. To get one of the photo ID cards I will need to go to the DMV where they will ask for proof of residency and so I will need to be added to her utility bills.
For her water bill she did call and they said that I need a photo ID, fill out Update Account Form to add me to the utility bill and to show proof of ID.
So I think what will do is get my SSN first, then once I get that go to the DMV for California Driving License ($45) or California Photo ID ($29), once received then get added to my fiancées utility bills and then apply for a bank account.