FORT WORTH — On the same day that the world’s elite cyclists embarked on their annual race along the winding roads of England, Mayor Betsy Price was front and center in a pack of more than 120 riders outside a popular local restaurant, poised confidently on her 18-speed carbon-fiber racing bike.

This was a scaled-down Texas version of the Tour de France, named the Tour de Fort Worth. Following Ms. Price’s ambitious pace, the cyclists stretched out along a 21-mile course under a brilliant midmorning sun, eventually regrouping back at the restaurant parking lot.

Ms. Price, who is 64 and a longtime cycling enthusiast, created the event three years ago as part of a “FitWorth” initiative to promote healthy living in a place more commonly associated with barbecue and thick steaks than with carrot juice and kale. Now one of her signature programs, the Tour de Fort Worth — which includes more than a dozen such rides through July — is just one component in her two-wheeled style of community outreach.

The mayor regularly swoops into the city’s disparate neighborhoods on her bike to conduct “rolling town-hall meetings,” taking City Hall to the people. Residents bike up next to her to discuss a variety of issues and grievances, like zoning, potholes and trash pickup.