BART’s flashy new trains finally crossed the bay into San Francisco this week, rolling their electric-blue seats and maternal, computerized station announcements from Warm Springs to Daly City.

Commuters have waited months to try the Bombardier model — a more efficient design and futuristic look for BART that’s been hobbled by technical challenges — as the agency moves cautiously toward deployment across its system.

Earlier this year, the transit agency debuted a 10-car train on the Richmond-Fremont line — the least busy in the system, and one that bypasses the Transbay Tube. It switched routes just as BART’s Board of Directors weighs whether to buy its second batch of new cars from the same company, a move that could save $350 million and a two-year bidding process, bringing the trains into service a lot faster.

BART has ordered 775 cars from Bombardier and needs an additional 306 to meet future demand. Thirty-five cars have been certified by the California Public Utilities Commission, and BART has approved 30 of them to carry passengers, though only 10 — the equivalent of one train — operate daily. The agency is using the other 20 to train its operators for a gradual two-month rollout: By the end of this year, officials hope to run five Bombardier trains throughout the system, one on each line.

Second new BART train spotted passing through S.F. today. This one, photographed at 16th Street Mission station, was Warm Springs bound. Morning train was also heading east out of S.F. pic.twitter.com/IRuxbLxvI6 — Don Clyde (@ClydeDon) October 22, 2018

By spring 2022, BART’s 775 Bombardier cars should be gliding throughout the system, along with a few relics from the older fleets. The plans also call for a new railcar storage yard in Hayward and five new traction substations to power all the new trains.

“The only thing that’s frustrating about these cars is that they’re not here yet,” said board Director Joel Keller, who represents east Contra Costa County.

Delivery of the Bombardier cars has been slower than expected, mostly because they have to be built from scratch, said board Director Rebecca Saltzman, whose district includes a long swath of the East Bay. BART was built in the 1960s to be a space-age, state-of-the-art system that ran on a unique track.

Since it doesn’t use a standard-gauge railway — a term denoting the international norm of 1,435 mm between rails — all of its equipment has to be custom-built and tested on BART tracks, not in a facility, said agency spokeswoman Alicia Trost.

“We can’t buy anything off the shelf,” she said, noting that BART is lagging on its timeline for installation of the new cars. It originally expected to have 198 of the shiny vehicles gliding across four counties by July. But the first shipment was beset by mechanical problems that required 202 visits to the shop — and an additional 279 for preventive maintenance.

“The major complaint I’ve heard is that it’s been slower than expected — that there aren’t enough of them,” Saltzman said.

Even so, she and other board members rave about the Bombardier coaches with their bicycle racks, bright blue-and-chartreuse seats, digital maps and three doors on each side for quick passenger boarding.

“It’s just a smarter design for our crazy urban environment,” said board Director Nick Josefowitz, who represents San Francisco. He praised the plastic seats of the new cars, which are more compact and easier to clean than their upholstered predecessors. Each car has five fewer seats than the older models, which means more people can stand during rush hour.

BART was designed as a hybrid of a subway and a classy commuter rail, in an era when transportation patterns were different: About 50,000 people rode each weekday, compared with 440,000 people today. Ridership is expected to swell to 770,000 by 2040, and the Bombardier generation may have to accommodate that growth. Agency officials will rely on the fleet’s Ethernet technology — along with a new systemwide control system — to increase capacity in the tube by 45 percent.

Keller said he’s seen glitches since the initial rollout in January, including digital maps that showed the wrong destinations, because the software wasn’t working. But he’ll probably support agency staff’s request to negotiate a contract extension with the company.

“I haven’t seen anything that’s a deal breaker,” he said.

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

Twitter: @rachelswan