Collision with CTA bus; experience with claims process?

I got in a collision with a CTA bus about a month ago in the Loop when it ran a red light on Madison and hit me. Fortunately, it knocked me away from the bus, so it just ran over my bike and not, say, my leg (RIP, bike). Miraculously, my injuries are no worse than a sprained wrist and some whiplash (in physical therapy now). I'm trying to get the claims process started now and haven't had much luck hearing back from the department. Has anyone had experience dealing with the CTA claims department? Any tips for speedy resolution? I imagine it's a different beast than a private insurer. I called the Active Transportation Alliance hotline and they didn't have any advice for the CTA in particular, nor did the lawyer.