Those sturdy red bicycles that have woven their way into the urban landscape in the District and Arlington could make their debut in Rockville by next year with the help of a $1.9 million federal grant approved Wednesday by the regional planning board.

More than 1,100 bikes offered by the Capital Bikeshare program already are being used by commuters, shoppers and tourists in Washington and across the river in Arlington, with riders choosing bikes from more than 110 secure docking stations.

The funding, approved by the National Capital Region Transportation Planning Board during a regular meeting, would be used to add 200 bikes and 20 docking stations in Rockville and Shady Grove. Because it’s unlikely that many people would pedal from Rockville into the District, most of those bikes would be used around town or to commute from home to Metro stations.

“I assume they are looking for funding before they approach us,” said Chris Holben, the District’s bike-sharing manager. “We’re very interested in what they want to do and in welcoming them to the Bikeshare family.”

The funding would come through a Federal Transit Administration program known as Job Access and Reverse Commute to provide mobility for welfare recipients and low-income people as they seek and hold jobs. Under the proposal, those who qualify would receive a free one-year membership, coverage for some user fees, a bike helmet and training classes, Montgomery County officials said.

“Bike sharing can be a cost-effective way to provide better transportation connections to low-income residents, many of whom hold multiple jobs and try to participate in job-training programs,” said Montgomery County Executive Isiah Leggett. “ . . . The Bikeshare program should significantly expand opportunities and improve the quality of life for all our residents.”

Proposed locations for the new stations include the Rockville and Shady Grove Metro stations, Rockville Town Center, along Rockville Pike, and on college campuses.

Capital Bikeshare has been made simple to use. Membership costs $75 for a year, $25 for a month, $15 for five days and $5 for 24 hours. Long-term members get a key to unlock bikes from docking stations; short-term members get a five-digit code for the same task. The first half-hour of riding is free. Fees kick in after that until the bike is returned to another docking station.

With the arrival of spring, the number of people holding annual Bikeshare memberships jumped from 10,700 in April to 13,835 by the end of May.

The commuter cycling culture, long a transportation mainstay in Europe, has flourished in the Washington area in recent years. The growth of bike-only lanes has served to encourage cyclists who might otherwise have feared doing battle with cars and trucks on congested streets. Office buildings and local governments have made more racks available to those who ride their own bikes.