I was waiting to turn right from a shopping center onto NB hwy 360 during rush hour. The sun was low in the sky and severely limited my field of vision. During the heavy traffic, another car left room for me to pull in. I waved to him as thanks and pulled forward blocking the shoulder, but not fully entering the roadway-- couldn't continue since all traffic was stopped. This left about 7-8 feet distance between me and the other car. I sat still. A few seconds later a bicyclist came from my left, seemingly out of nowhere, going very fast down the shoulder. He swerved around me and lost his control in front of my car, flipping over his bike and falling off. Later he explained that he thought I was waving at him to pass me. No cars were moving, including me. What does the law say about this?
The law does not give a strict answer to this kind of question. What happens in law is that the law provides conduct duties and a jury decides in a given case whether a duty was not met. The duty that applies to injury cases is that the people involved must use that same level of being careful that a reasonable person would have used under similar circumstances. If someone fails to do that and someone else gets hurt as a result of that failure, then the injured person can recover for the injuries.
As long as you acted like any other reasonable person would have acted, then you are not liable. So I cannot give you an exact answer, except to say that, if it was just a mistake on the part of the bicyclist in misinterpreting your wave, then maybe no one was legally "at fault."
You should notify your insurance company, and let them handle things, though. And don't worry, they won't pay if it was not your fault (they try not to pay even if it was).