I remember years ago I was in the same situation being assigned at Ramstein and PCS to Andrews. Although I resided in the base and eventually Clinton, I had send for a NJ out of state registration for my VW GTI.
My home state was NJ and had that special tax exemption ruling since the car is not garage there.
Im sure you can do the same with your home of records (CA) and do the same.
Being Active Duty provides you with alot of special programs. I just wish now I still have the VA Property Tax exemption on my cars but I dont since Im already out.
Good Luck and lets also wait for other responses.
Bethesda is a cool town, alot of high end cars there btw you are lucky!!!