A week after the dockless bicycle arrived in Washington, Toby Sun was already talking about the possibility of demand so high that the city would need thousands of them — 20,000 to be exact.

“It is a big city. A lot of usage,” said Sun, chief executive and co-founder of LimeBike, one of the four companies that launched dockless bike-share operations in the District last month. “If we truly want to have a bike-share system that people very conveniently use, and more instead of driving, we need to have the coverage,” he said.

Washington’s fascination with biking is already taking the city to new levels.  Nearly 5 percent of D.C. commuters make their trips on two wheels, according to census data. This puts D.C. on pace to surpass Portland as the U.S. city with the highest share of bike commuters.

So far, Sun said, Washington has responded as projected to the new high-tech bike services.

“We are already seeing D.C. has great usage,” Sun said.

Each LimeBike bicycle was used more than three times a day on the introductory days of service. One bike was so popular it was ridden 39 times. One user loved LimeBike so much he or she made three trips each day.

There were 2,800 users and over 5,200 trips during the inaugural week.

The new companies combined have more than 1,200 bicycles on city streets. LimeBike, and its competitors Spin and Mobike, say they each have deployed 400 bicycles, the maximum number allowed under city permits. Another service, Jump, had 50 bikes on the ground last week and in the next few days will phase in an additional 120.

The region’s Capital Bikeshare program, which operates as a station-based system, has a fleet of more than 4,000 bikes.

Officials with some of the bike companies say they expect the 400 cap will rise as usage and demand grows. Seattle, the first city to allow dockless systems, has raised its limit since the programs began operations there over the summer. The District Department of Transportation said it is allowing dockless bike services to operate in the city as part of a six-month pilot program.

The new bikes have been gracing the city’s downtown sidewalks since Sept. 20, although some have already been spotted across all eight wards.

Sun said he personally delivered 50 of LimeBike’s green bikes on Sept. 23 to Southeast Washington, where, he says, his company wants to make bike-share available in the District’s poorest neighborhoods.

Sun said his company also aims to help cities mitigate first- and last-mile commute challenges. In its first week in D.C., LimeBike ridership was as strong as it is in Seattle, where the company has been around for a couple of months now.

Rides in D.C. averaged about 8.5 minutes and 1.13 miles. The usage, LimeBike says, translates to 104,000 calories burned and 102 gallons of gasoline saved.

“We are optimistic that with continued growth, we will be able to complement existing transportation to even better serve locals and visitors in broader D.C. communities,” said Sun.

LimeBike launched in San Mateo, Calif., in January with $12 million in venture capital. The company was the first dockless concept introduced in the United States, making its first stop in May at the University of North Carolina at Greensboro. Now it has its green bicycles in nine U.S. cities and seven college towns.

Now their mission is to deploy as many as 70,000 bicycles across the U.S. by the end of the year, said Sun, a former investor at Kinzon Capital.  And they anticipate the District will require a much larger fleet of bikes than currently allowed.

Said Sun: “Four hundred is not enough. For this market, at least 20,000.”