I know that a hit and run is a misdemeanor in California when there are only property damages, but does this also applies to a collision in a private property? How is a typical bump in a parking lot handled by California law?
California Vehicle Code §20002 et seq deal with hit and run property damage to vehicles. The first sentence of this section defines its application:
(a) The driver of any vehicle involved in an accident resulting only in damage to any property, including vehicles, shall immediately stop the vehicle at the nearest location that will not impede traffic or otherwise jeopardize the safety of other motorists...
No statement later in this section, or in a subsequent section, restricts its operation to public streets or rights-of-way.
California hit-and-run laws apply, therefore, to both public streets and to private property.
In this day and age, if you notify law enforcement, you're very unlikely to get any police interest or response. You can report the matter to your own insurance company if you wish, and investigate on your own. If you have clues or evidence identifying the offending vehicle or driver, you could proceed against them in Small Claims Court.