All you have to do is contact the housing authority who handles your current Section 8 benefits. Inform them that you are looking to move to the Bay Area. If you have what is called tenant-based assistance, they have to contact the housing authority that covers the area you wish to move to and, as far as I understand, that housing authority has to issue you benefits. If, however, you have project-based assistance, meaning that your Section 8 benefits are attached to your housing unit as opposed to you, then you would lose your benefits if you move. This does not mean that you cannot reapply for benefits in the Bay Area, but you will most likely be faced with waiting lists, etc.
I hope this helps. And best of luck!! I hope it works out for you.