I teach traffic school in California, when I’m not at my day job. While I’m not a complete expert, or an official authority, here’s my opinion. From your description of what happened, the other driver is at fault. As for the police, you are only required to report the accident to the CHP/police if someone is injured or killed. However, if there’s anything other than a slight ding, getting a police report will help with insurance.
Also, if there is any property damage over $750, you must file an SR-1 form with the DMV within ten days (an SR-1 is also required if there’s any injury or death involved). Even though insurance companies may do the paperwork, ultimately it is your responsibility to file it. You can have your license suspended for up to a year if you don’t file the SR-1. You say the bumper damages are $600; if that’s the only damage, no SR-1 required. But if there’s additional damage, make sure it’s filed ASAP.
It’s now after the fact, but regardless of whether the police come or not, taking pictures of the accident scene/damage is strongly advised. If you don’t have a camera, make a sketch on paper. It’ll help when you report the accident to insurance.
Good luck with filing the claim!