Bike sharing got off to a slow start in San Francisco, but it’s about to explode, with two startups vying to take on Bay Area Bike Share, which itself is embarking on a major expansion with $49 million in funding from Ford Motor Co.

Bay Area Bike Share is operated by Motivate, a New York City company that runs programs in 10 other metropolitan areas including New York, Chicago, Boston and Washington.

The bikes are designed for quick trips around town. Users can check out a bike from one docking station and return it to any station. In San Francisco, they can buy a membership for one day ($9), three days ($22) or one year ($88). Users can take an unlimited number of 30-minute trips during the membership period. If they don’t return the bike to a station within 30 minutes, they will incur overtime charges up to $7 per half hour.

Kitty Steinborn of San Jose picks up one of the baby blue bikes to get from the Caltrain station in San Francisco to her once-a-week teaching job at the University of the Pacific dentistry school a mile away. “I love being a hip 61-year-old biking to work in a skirt and tights even in the rain,” she said. Only twice in two years was there no bike at the station or a slot to return it to the rack near the school. On those occasions, she had to use another station and was late for work.

The Bay Area program began in 2013 with about 700 bikes and 70 docking stations in San Francisco, San Jose, Palo Alto, Redwood City and Mountain View. Use in the latter three cities was so low that the program was discontinued.

Today, there are 300 to 350 bikes and 43 stations in San Francisco. San Jose has 130 bikes and 20 stations.

A study published on the website Priceonomics last week compared San Francisco’s bike share program with those in five other big cities, all operated by Motivate. It ranked the programs on factors such as bikes per 1,000 residents, bike stations per square mile and trips per bicycle per day. In all three categories, San Francisco ranked last or next to last after Seattle, whose program is being shut down.

“San Francisco is often thought of as a bicycle mecca. But when it comes to bike sharing, so far the city lags far behind other successful systems,” the report said.

Priceonomics says it makes money “by helping companies turn their data into content marketing that performs.” It did the ride-sharing report for its client Spin, which wants to start a bike sharing business in San Francisco.

Heath Maddox, who manages the bike-sharing program for the San Francisco Municipal Transportation Agency, called the report “fake news. It is literally a spin piece to try to make what they want to do better than what we have done.”

Maddox disputed some of the report’s numbers. A report published by the Transportation Research Board said that for the year that ended Aug. 31, 2015, San Francisco’s bikes were used 2.5 times per day on average.

The Priceonomics report initially said that for the year ended Sept. 30, 2016, San Francisco’s bikes were used less than once, or only 0.8 time per day. After a call from The Chronicle, Spin rechecked its numbers and revised that to 1.7 times per day.

To calculate bikes per capita, Rohin Dahr of Priceonomics said it relied on Wikipedia. That entry vastly overstated the number of bikes in San Francisco.

No matter how you crunch the numbers, San Francisco’s program is small for a city its size. It was started as a pilot program with public funds, but there was no money to expand it. New York’s Citi Bike program, started around the same time but with major funding from Citibank, now has about 10,000 bikes.

“We think San Francisco is a fantastic town for bike share,” said Dani Simons, a spokeswoman for Motivate. She said the Priceonomics study is irrelevant because “with the expanded program, San Francisco will have the most bikes per capita of almost any city in the world.”

Thanks to Ford, the Bay Area program will begin expanding this spring. By the end of next year, it expects to have a total of 7,000 bikes and 550 to 700 stations in San Francisco, San Jose, Oakland, Emeryville and Berkeley. San Francisco alone will have about 4,500 bikes.

The program, and the bikes, will be rebranded Ford GoBike. The new bike made a cameo appearance in Ford’s Super Bowl commercial this year.

Ford “is very interested in people perceiving them as a mobility company, not just a car company,” Simons said. In September, Ford bought San Francisco commuter-shuttle startup Chariot.

Motivate hopes to find secondary sponsors that could advertise on the program’s app or stations, but not on the bikes. The expansion will get no taxpayer dollars.

Today, San Francisco’s program covers only 3 square miles of downtown San Francisco. After the expansion, it will encompass 23 square miles — almost half the city. It will be concentrated in the northeast quadrant, and won’t go on hills where the grade exceeds 7 degrees.

Motivate’s contract with San Francisco and other participating cities gives it exclusive rights to operate a bike share program on public rights of way, with certain exceptions. “Exclusivity is a provision that some cities have granted in exchange for us to agree to (certain) provisions,” Simons said. For example, it agrees to “rebalance bikes around the city” so they don’t congregate in one place, and to make sure they are “in safe working order.”

That exclusivity is being challenged by startups such as Spin and Bluegogo. They want to do station-less or free-range bike sharing, which lets users leave a bike almost anywhere and find and unlock it with a smartphone app.

In China, station-less bike sharing has attracted so much capital, and dumped so many bikes on crowded city streets, that it’s creating a backlash.

Bluegogo, a Chinese company, raised $58 million last week, bringing its total funding to $88 million; SpeedX, a Chinese bike maker, is an investor and supplier, said Ilya Movshovich, the company’s U.S. vice president.

Bluegogo’s plan to drop hundreds of bikes on San Francisco sidewalks without permission enraged city officials. The company changed its plan, and is now operating out of 15 private parking lots with just under 200 cobalt-blue bikes. The company hopes to let riders drop them off at public bike racks in the future, and even offered to pay for more racks, Movshovich said. The cost is 99 cents for every 30 minutes, with no membership required.

Bluegogo got a business license Jan. 24, but the city says it still needs a permit to operate a “retail sales or service business” on private parking lots, Movshovich said.

Derrick Ko, a former Lyft product manager who co-founded Spin, said he is talking with city officials about starting a station-less bike sharing operation in San Francisco. The local startup, which has not announced any funding, has close to 1,000 orange bikes, which it plans to begin rolling out this month in “launch cities” that Ko won’t name.

Maddox said the city’s transit agency is working with Supervisor Aaron Peskin’s office on legislation that would create a new permit for station-less bike share programs that will include conditions to protect the public.

Most people agree that San Francisco’s current system is too small to be viable. “When you have citywide systems, which San Francisco does not yet, the thing that is most important to broad adoption is density. I think there is potential for it to be hugely popular if it is expanded properly,” said Chris Cassidy, a spokesman for the San Francisco Bicycle Coalition.

Daniel Menzies, who lives on Treasure Island and commutes into the city by bus, uses bike share to get to his job as ... a bike courier. He keeps his own bike locked up overnight at an Embarcadero BART Station facility because it’s safer than keeping it at home.

What would make bike share better, he said, “is more stations. I think there should be one on every city block where it’s practical. It would be so convenient people would have to find reasons not to use it.”

Kathleen Pender is a San Francisco Chronicle columnist. Email: kpender@sfchronicle.com Twitter: @kathpender