http://www.bar.ca.gov/80_BARResources/07_AutoRepair/Auto_Repair_Guide.html states that they were supposed to give you a written estimate.
By Law, the auto repair shop must provide a written estimate before doing any work. Ask if there is a charge for the estimate. After you have received the estimate, feel free to go to another shop for a second opinion.
A written estimate must include the total estimated price for parts and labor for a specified repair or service. The estimate must also itemize the parts to be used and the method of repair. The repair shop must stick to the method of repair and the parts listed unless you agree in advance to any changes.
In addition to the total amount, the estimate may itemize the parts to be used and the method of repair. If so, the repair shop must stick to it. They may not legally substitute parts or change the repair method without your consent.
The technician will ask you to sign the estimate/work order, which gives the shop permissionto proceed with the work. If you want any of the parts returned to you, be sure to say so when the technician gives you the estimate.
If the technician later determines that it will take additional work and will cost more to fix your car than the original estimate, someone from the shop must contact you, describe the additional work and cost, and get your permission to proceed.
It was improper for the shop to not give you a written estimate and that is grounds to complain to the BAR.
https://app.dca.ca.gov/bar/complaints.asp has the complaint form.
Or, you can file in small claims court for a refund based on the lack of a written estimate.
Am I correct in assuming that the verbal estimate was substantialy less than the actual bill?