Actually, there is a very nice way to get to the coast north of San Francisco and come across the Golden Gate Bridge. I understand your reasons for doing so.
When you get to Davis on the Western Express, continue on only as far as Winters, then take Hwy 128 over the ridge to the Napa Valley (famous for its vineyards) and Silverado Trail south to Napa. From Napa there are a series of back roads to Petaluma that let you avoid most of Hwy 121 and Hwy 116 - Old Sonoma, Hwy 121, Napa, 5th, Watmaugh, Arnold, Hwy 116, Adobe, Washington. From Petaluma, take Point Reyes Road to Hwy 1 on the coast. Point Reyes has some spectacular backcountry campsites on the coast, but they require reservations, I believe. Weekends might be tough, but a weekday night may be possible, even just a day before. Point Reyes is off the main route; however, there is also a backcountry campsite right on the cliff at Golden Gate just north of San Francisco.
Anyhoo - you can then follow Hwy 1, the Pacific Coast Bike Route, south to the Golden Gate Bridge - remembering to get off the main highway in Sausalito and follow city streets and trails. It is generally well marked - or you can get the map section from ACA.
Have a great trip - J
PS - You do know that Nevada is empty and will be hot by late July or August, non? If you have toured in Morocco or Algeria, you may have encountered something similar - except that there are way more people and villages in North Africa. Vide. Leer.http://www.nps.gov/pore/planyourvisit/camping.htm