The most common bicycle accident we get called about is exactly your situation: a bicyclist who rides from the sidewalk into a crosswalk and is hit by a right-turning car. The driver's attention is focused on vehicles approaching from his left, as he waits for traffic to clear, so he doesn't notice you approaching from his right.
If the accident happened in Santa Monica, the city prohibits riding bikes on the sidewalk. So you were coming off a place you weren't allowed to be riding. This is referred to as "comparative negligence case," i.e., you and the motorist each bear some fault for the accident. The percentage of fault depends on the eye of the beholder. The insurance company will put all or a large percentage on you. A personal injury lawyer will look for facts to help put the majority of fault on the motorist.
Whether a lawyer would be willing to take your case, knowing going into it that you bear some percentage of fault for the accident, depends on whether your injuries are serious enough and your medical bills (and lost wages?) are high enough to make it a worthwhile case for the law firm to pursue.
If you are a bicyclist who was hit by a right-turning car, you are welcome to call our office for a free consultation. We will give you opinion on the strength and value of your case.