I have had a few close calls. My left thumb has saved me. I use my horn all the time. If I think there is a possibility of someone pulling out in front of me, I hit the horn and point at them. That usually gets their attention. Last summer I had a woman who walked down the road towarss me, got in her car parked on the same side as I was going, then just pull and u-turn right in front of me. I went from 55 to 5 in a hurry. If I hadn't mashed the horn, she wouldn't have stopped in the middle of the road allowing me a tiny bit to slide by. I showed her that she was "number 1" when I realized that I wasn't going to superman over her car... Less than impressed.
Just drive like everyone in a car is out there to kill you. Don't drive scared, just really defensively. Stuff like not riding in blind spots, not doing a billion miles an hour in traffic, not stopping in traffic to make a left turn. Think and drive smart. Don't assume that they saw you or even if they did that they will yield to you.
Also, don't be scared of bikes. They are actually really stable. The faster you're going, they more stable they are. Practice going slow and starts and stops. Any idiot can go fast. It's the slow stuff that's hard.