Can I charge the insurance company for my time and costs dealing with a claim?

A property damage claim includes the cost to repair or replace the vehicle and compensation for loss of use of that vehicle. Insurance policies define this property damage as to amount they will pay on behalf of their insured. There is not doubt that any accident is an inconvenience for everyone involved, however, the insured person’s policy probably won’t compensate you for time or lost wages under a property damage claim. Currently there is no law or case law that addresses this issue. This matter is often settled through Small Claims Court.

From: Washington Insurance Commissioner Fact Sheet