San Francisco startup Scoot, known for its fleet of red electric mopeds, wants to add e-bike rentals in the city.

But it can’t. San Francisco won’t issue any more permits for dockless e-bikes until summer 2019 at the earliest. Only Jump Bikes, which was recently acquired by Uber , has permission to offer dockless e-bikes in the city , under an 18-month trial program.

It’s a big disappointment for Scoot, which argues that it played by the rules before putting its rental fleet of 650 electric scooters — resembling Vespas, unlike the recent wave of stand-up e-scooters — onto city streets five years ago.

“The name of the game at Scoot is fast, affordable, electric mobility,” said Scoot founder and CEO Michael Keating, sitting in the company’s South of Market office/garage where the battered wood floors are splashed with paint from its previous use for building stage sets. “We want to give people a way to get around the city quickly without having to drive or be driven.”

Unlike e-scooter startups Lime, Bird and Spin, which generated huge controversy by plunking their scooters on city streets with little warning and only now are going through a permitting process, Scoot helped craft its own permit before starting moped service in San Francisco and pays the city for parking rights. Although mopeds can legally be parked on sidewalks, it specifically refuses to so that the bikes won’t block or annoy pedestrians.

“We want to bring that spirit to e-bike share in San Francisco: Do it the right way, responsibly,” Keating said. “Even though we’re not happy we weren’t able to launch our e-bikes here, we won’t break the law. We’d rather the city allow us to operate in the appropriate way.”

As Keating tells it, Scoot was working on its application for e-bike sharing in December 2017 when word came that Jump had been granted an 18-month exclusive permit. “We don’t want to wait that long,” he said. “We are being persistent.”

The San Francisco Municipal Transportation Agency tells a somewhat different story.

It said Jump was the only company to fully complete an application for dockless e-bikes, after the application was posted in June 2017. The MTA decided to give Jump an 18-month permit as a pilot to “evaluate, collect data and assess whether further increases would serve the public interest,” said spokesman Paul Rose.

Although he said Jump was not granted exclusivity, the reality is that it will remain the only legal dockless e-bike renter for 18 months. (“Docked” e-bikes were recently added in the city by Motivate’s Ford GoBikes; these must be parked at specific stations.)

“We are not currently reviewing any stationless bike-share applications, nor would we consider issuing any additional permits during the 18-month pilot period,” Rose said. The MTA has used similar pilot periods to evaluate other new technologies, such as on-street car sharing and Scoot’s electric moped sharing.

Still, Rose said, “Scoot has been a successful and good partner for emerging mobility services in San Francisco.”

Chris Cassidy, a spokesman for the San Francisco Bicycle Coalition, said he’s eager to discover what the city learns from the Jump pilot. “Seeing more people have access to electric-assist bikes is better for all of us, it makes for better air quality and more-affordable transportation options,” he said.

Whenever Scoot can win the city’s approval, it wants to rent out the e-bikes, which top out at 20 mph, for $2 for the first 15 minutes, then 10 cents a minute.

Like Jump’s e-bikes, those from Scoot will include a built-in lock so users will secure them to racks or poles rather than leaving them helter skelter — one of the issues with the stand-up e-scooters.

Keating says Scoot will figure out a way to include a helmet with each bike, as it does with its mopeds. Helmets are legally required on e-scooters and some e-bikes, but no company in San Francisco currently offers them packaged with either vehicle, although Bird will mail a free helmet to any San Francisco user who requests one.

Scoot also wants to offer a community benefit: adding more bike racks citywide, for all riders.

Keating said Scoot will bring as many e-bikes as the city allows. Jump is capped at 250 bikes with an option to double that after nine months. Jump CEO and founder Ryan Rzepecki told The Chronicle last month that he’d like to increase his fleet size sooner, but the MTA said it’s sticking to that timeline.

Meanwhile, Scoot is expanding for the first time outside San Francisco by bringing 1,000 e-bikes and 500 mopeds to Barcelona, Spain, a city of 1.7 million with a strong affinity for motor bikes and motor scooters.

The e-bikes will serve double duty as pieces of public art, thanks to vibrant murals wrapped around them with images by Barcelona artist Mina Hamada.

This story has been corrected to clarify helmet requirements for e-bikes.

Carolyn Said is a San Francisco Chronicle staff writer. Email: csaid@sfchronicle.com Twitter: @csaid