Some California traffic laws do include bicycles. VC 21200 says:
Every person riding a bicycle upon a street or highway has all the rights and is subject to all the duties applicable to the driver of a vehicle, including the provisions of law dealing with driving under the influence of alcoholic beverages or drugs, except those provisions which by their very nature can have no application.
It is the same thing with water craft. In fact if you are under age and get caught riding under the influence 21200.5 says they can fine you and hold back your drivers license for a year.
VC 21800 says you can run a red light but only after stopping and only if it doesn’t change or doesn’t work. Because that applies to all vehicles I am guessing you could be cited and it would be a moving violation.