I'd go ahead and file in small claims court. Filing fees are not typically very high. Odds are reasonable the insurance company will then pay you for the bicycle; I am skeptical that you will collect for time lost but it may not hurt to ask.
I went to small claims court a number of years ago after a motorist's insurance company repeatedly "lost" my claims. They miraculously found everything the day before the court date and agreed to pay if I did not make them go to court. (I went to court to avoid a loss by default.) I will admit my case was more typical (i.e. easier for judge to understand) - I was suing for damage to a parked car hit by the defendant.
When I was hit on my bicycle, AAA asked many questions before agreeing to pay. I think it was a combination of incompetent police, incompetent insurers, and stalling.
By any legal standard, if your motorist was making a left turn s/he legally should have yielded. In actual observation locally, different police officers and judges have different rules when bicyclists are involved - many think bicyclists do not have legal rights to use the road and are automatically at fault, while others apply the law as written. Again, you have little to lose, but be prepared to explain the law very carefully and simply.
From my experience, your claim is so small the insurance company won't defend in court, and they will pay you in 2-3 months. If you can't afford a cheap bike off Craigslist in the meantime, you are probably SOL for time wasted (hence you want to file now).