Bring your old license, that bill that proves where you live, and the 2nd ID of the BC and you're golden. Next stop is the local Medicann and $65 later you are good to go.
I would suggest getting the CA state card as that can't be refused as proof of medical need by law enforcement. It cost me $125 but the peace of mind it gives me is priceless.
The ASA website has info for various counties in CA so check it out.
Take a ride to an out-of-the way rural DMV office and hang out, it can't take longer than 2 hours.