Back when I first started cycle commuting, I used to worry about it when I was awake in bed... I could easily imagine getting run over all different ways, by cars I couldn't even see. But once I actually was on the road, I always felt comfortable because I only had to manage a few cars at a time... so it felt quite safe.

I too ride in a suburban area where bicycles are fairly rare. Sometimes you just have to take the lane for your safety. I do this quite often, and only move right when it is safe to do so. A mirror helps manage this much easier. I also communicate with drivers with various hand signals.

No one wants to hit you, don't allow them to pass when there's not enough room to safely do so.

Drivers will get to know you, and you'll get more comfortable with some time on your route.