"California vehicle code section 24016 (b,) subdivision3: A person operating a motorized bicycle is NOT subject to the provisions of this code relating to financial responsibility, driver's licenses, registration, and license plate requirements, and a motorized bicycle is not a motor vehicle."
Now here's the catch. Although the code is written for both 406a (electric) and 406b (gas) it doesn't seperate the two. Other VC sections pertaining to gas powered bikes override the the registration, license, and it not being a "motorized vehicle."
But according to the cops I've talked to, there is no VC that says a gas powered bike HAS to have insurance.
It appears that when that section was written in 1995, they forgot to make that distinction.
So, legally, you don't need insurance.
But for a gas bike, you do need at least an M2 license (or permit,) a DOT helmet, registration, license plate, headlight, taillight, brake light, horn, and left mirror.