We believe you are referring to the FasTrack which is an electronic toll collection (ETC) system used in the Bay area of California that allows you to prepay your bridge tolls, eliminating the need to stop at the toll plaza. The system has three components: a transponder, which is placed inside your vehicle; an overhead antenna, which reads the transponder and collects the toll; and video cameras to identify toll evaders.
This is CA system comparable to the SunPass used in parts of Florida for toll roads or the Illinois' Open Road Tolling program where I-PASS or E-ZPass users continue to travel at highway speeds through toll plazas.
You can try to fight your ticket in court by stating to the judge that the signage showed that FasTrack was okay in the lane you were using. You would likely need to show photographic proof of this sign and its location. You can speak with a traffic ticket lawyer to see if they can give you any advice on how to prepare for court and what exact proof may allow you to get your carpool ticket dismissed.
You may also be able to get information on if this ticket may be dismissed based on your understanding of the sign you read by speaking with court listed on your ticket. Sometimes clerk of the courts will be able to help you with questions you have regarding your citations. If you cannot get the ticket dismissed then from our research it appears a carpool or ticket for incorrect use of a HOV lane is around $380.
To get auto insurance quotes online for San Francisco or any other area of CA, follow this link.