California is fixing a gap in its license plate law that enabled drivers to cross bridges and coast along express lanes for free, costing the Bay Area nearly $13 million a year.

Starting Jan. 1, the free rides are over. Every new or used car will have a state plate with a unique string of numbers before it rolls off the dealership lot.

Proponents say the change will save money and help solve crimes. Many cheats who breeze through tollbooths sport the cardboard dealer logos that serve as a placeholder on new cars, rendering them anonymous. Some get in crashes and flee the scene.

“When you get new plates, you’re supposed to put them on immediately,” said Jaime Garza, a spokesman for the state’s Department of Motor Vehicles, referring to the current law.

But in reality, he said, drivers use the varnished dealer placards indefinitely.

“It causes big problems because people run red lights, and they’re involved in accidents, and we can’t trace their plates,” Garza said.

The new temporary license plates will display an expiration date 90 days after the sale of the car and link to a Department of Motor Vehicles database that identifies the buyer and includes a description of the vehicle. The DMV will send permanent plates with new numbers to replace the temporary ones.

Assemblyman Kevin Mullin, the San Mateo Democrat who wrote the law, said he wants to help highway patrol officers and stop toll evasion, which siphons money from Bay Area transit. In 2016, more than 2.5 million vehicles passed through FasTrak lanes at the seven state-owned bridges without license plates or toll tags and without stopping where possible to hand over cash — a nearly fivefold increase from a decade ago.

“As someone who drives back and forth from San Francisco three times a week during our legislative session, I routinely see cars driving in the express lanes with dealer advertiser plates, or no plates at all,” he said.

Mullin noted that license plates have taken on new importance as transit agencies ring the Bay Area with tolled express lanes, a revolution in freeway travel that’s required a new form of enforcement. Regional transit officials are shifting to an all-electronic system, ripping out tollbooths and replacing human toll collectors with plate-reading cameras.

More importantly, Mullin said, temporary plates solve a public safety quandary. Without the identifier of a license plate, police have no way to track hit-and-run assailants. As a result, they’ve left high-profile cases unsolved.

Mullin said he was particularly stung by the 2013 death of 35-year-old pedestrian Michael Bonanomi, who was struck by a white Mercedes as he crossed Ventura Boulevard in Los Angeles. He flew onto the car’s hood and then toppled to the ground as the car sped off. The driver had dealer plates and was never apprehended.

“When I was made aware of that tragedy, it became clear there was a gap in public safety with regard to these dealer advertiser plates,” Mullin said.

Dealership customers can still order vanity plates, according to Mullin’s office.

But the transition won’t be easy.

While other states have already implemented temporary license plate rules, California has allowed dealer placards for so long that they’ve become part of the culture. In some areas, the dealer ads are a status symbol because they make a car look new, Garza said.

He noticed a lot of cars with dealer inserts when he lived in Los Angeles a decade ago.

“You’d see people buying a car from an auction, picking it up and keeping these plates on forever so it looked like the car was new,” he said. “Apparently in some areas a new car is really prestigious.”

Car dealers also liked the inserts because they served as mini advertising billboards. Under the new law “we’ll lose that exposure,” said Terry Furusho, a finance director at Serramonte Ford in Colma.

Furusho has spent several weeks preparing for the transition, which will start this week in Serramonte’s showroom and lot. The cars and trucks parked there have identical cardboard inserts with the Ford logo printed in royal blue.

On Friday, Serramonte employees gathered in a small conference room for their second tutorial on the new system. They passed around a piece of heavy-duty paper of the same size and material as the new plates — sturdy and white, able to withstand fierce sunlight or spattering rain.

Some managers are nervous. The dealership had to make various adjustments, purchasing four new laser printers and teaching the sales staff to report sales to the DMV electronically. The new law allows them to pass clerical costs on to customers by increasing document fees from $80 to $85 for each automobile purchase.

Now they have to explain the change to people who might resist.

Among the questions that came up Friday was how to handle customers who don’t want a front plate — which is required by law, but previously wasn’t the dealer’s responsibility.

“People who buy a Shelby Mustang might not want holes drilled in the front bumper,” Furusho said.

Next month those motorists will have to leave the lot with front and rear plates, or risk getting fix-it tickets and fines ranging from $25 to $197.

That satisfies Mullin, who said that people don’t just flout the law for cosmetic reasons — some motorists receive their permanent plates in the mail and then toss them in the back seat so they can cheat tolls.

“When they get pulled over they say, ‘Oh officer, I have my plates right here,’” he said. “Well, we’ll put a stop to that.”

Rachel Swan is a San Francisco Chronicle staff writer. Email: rswan@sfchronicle.com Twitter: @rachelswan