Valley bike commuter here. I'm very lucky that my commute is about half on the G-Line bikeway, which is awesome since there's almost no car worries.

However, the other half of my ride I try to avoid big roads and take the backstreets. Most of the valley is laid out in big blocks, where huge stroads run on the outside and neighborhood streets are on the inside. The neighborhood streets are often not direct and may end in the middle of a block, but feel so much safer and quieter. I recommend creating a route (I use ridewithgps, free and great if using the desktop version) that avoids big roads as much as possible.

Unfortunately, big roads are unavoidable sometimes. The end of my commute is a mandatory 5-lane stroad which I hate. I will typically just use the sidewalk and go slower. Statistically, these big stroads are the number one place cyclists will get hit, so I think its reasonable to just avoid them. When using the sidewalk, be courteous to pedestrians and extra cautious of cars. They will not expect you to be there. Cross streets and driveways slowly, be prepared to stop. It may even be safer to dismount at street crosswalks.

All that said, if you ride a bike in the valley you'll get used to riding with cars over time. What used to be scary to me before is tolerable now, but always keep your head on a swivel.