I'm sure it's more complicated than what I say, but I think ambulance companies will write a list of promises, the hospital or county might say what they want, and agree on a price. If the ambulance company gets the contract, they'll usually respond to that hospital. In you area,
Sutter Summit Pavilian, Alta Bates, Stanford/LPCH - ProTransport-1
VMC, Doctors - Westmed
Regional (and I think Washington) - Royal
St. Rose - Norcal
Kaisers in Santa Clara, Alameda, and Contra Costa County - Rural/Metro
911 in your area,
Santa Clara County - Rural/Metro
Alameda County - Paramedics Plus
Contra Costa County - AMR
A least for these county biddings for 911, the put a lot of the documents and agreements online. When I get home, I'll post a link to it so you can see what they discuss.
Not all areas work like this. I've been in areas where you start an ambulance company, the county draws a little border around your station, and says that you have to respond to 911 calls within that border so you might see multiple ambulance companies responding to 911 calls in the county.
Also if there was a fire department doing transport before counties were given the responsibility to deal with EMS, those fire departments can continue transport. Examples are Albany, Berkeley, San Ramon, Alameda, Piedmont, and Palo Alto Fire. From what I am told, it's difficult to get fire to do transport because it's the cities that got to agree on it. A lot of counties don't have funding for EMS cause they are only able to tax limited things too. Another issue is that Fire would no longer be able to do dual role since they'd be outra service for awhile cause of transport.
Edit Here is a link to all the information on the bidding in Alameda County.
http://www.acphd.org/ems/about-ems/paraplus.aspx