The accident statistics do not back up your assertion. Most cyclists are injured when turning from the wrong lane or when using bike paths or sidewalks. When you're on the road with the rest of the vehicles, people pay attention to you because they have to check to be sure that a car is not where you are. (There are bad drivers, but you have better maneuverability and brakes than them.)

Americans are taught at an early age to be afraid of riding their bikes on the street, but there is really nothing scary about it. And drivers aren't as bad as you think they are: when there is something in their path, they tend to steer around it.