I ride rural roads by myself all the time, and in defense of my country neighbors, with very little exception, I have found drivers to be cautious and courteous. For one thing, it seems almost everyone knows someone who rides now, so that inspires care. Also, rural drivers are used to unusual stuff on the roads - tractors, horses, wildlife, big ol' LLB on her bike again.
I think it's VERY important to be visible (see my post about unsafe jersey colors?) and I also avoid rush hour, when traffic is heavier and faster and drivers are sleepy/hungry/more distracted. I start my weekday summer rides at 6pm and have the roads to myself, also Sat & Sunday mornings, it's like riding through a ghost town.

2 tips - ride where your right tire would be if you were driving your car. It keeps you more visible, and gives you a little wiggle room for moving to the right even if there's no shoulder tot he road. Keep your eye (and mind )on the road no matter how breathtaking the scenery. If you start to get into a spot of trouble, LOOK WHERE YOU WANT TO GO and pedal yourself there! I wish I'd known this one right away - I learned the hard way that if I look were I don't want to go, that's exactly where I'll end up...maybe literally!

And I'm STILL in the process of riding where I feel safest and adding new roads gradually. If I start to feel "iffy" I listen to my intuition and head back to a one of my "steady" roads. and when I'm having a strong, confident ride that day, my bike will want to wander a bit, and I'll give her her head.