I don't know if the bridge(s) have been rebuilt yet on Highway 1. Yes, it's a gorgeous road, but maybe not if driving a new-to-you bus around its tight curves and gradients. I would definitely think hard about driving any bus there at the best of times. And as for staying invisible, I've never seen a yellow school bus there, so it would definitely attract some attention! Just go down 101 if you can deal with San Francisco city traffic at its north end, or 580 and 5 if you want a direct but boring route south. The latter however will require going over the Altamont and Grapevine passes, so make sure your cooling system is in good condition, and know how to safely descend the Grapevine's long 5% southbound grade if you don't have Jake brakes (trucks end up in the runaway ramps there all the time).
My bus is still registered as an Auto, which strictly speaking requires a non-commercial Class B license because its GVWR is over 26,000 lbs. When you have a Housecar, or whatever California now calls motorhomes and RVs, you are exempt from needing a Class B unless it is over 40 feet long. (Apart from the Ikarus bendy-Crowns and a few home-made articulated Crowns, no normal Crowns are over 40 feet long.) Just drive it sensibly, don't speed, don't make smoke from the exhaust, act like a real school bus driver, always use your turn signals, and stop with your 4-ways on at every railroad crossing (even though as a private bus you don't need to), then you'll be fine. And if you're stopped, just claim diplomatic immunity!
Good luck, John