“Can you see how quiet she gets?” said Suzanne Vullers, 51, an accountant turned equine therapist who co-owns the bed-and-breakfast with her husband, Rudi Vullers, also 51. “That’s what we’re looking for,” she said. “For the person and the cow.”

Hailing from the rural town of Reuver, in the Netherlands, the pair came across “koe knuffelen,” which means “cow hugging” in Dutch, on a return visit to their homeland two years ago. In parts of the Netherlands, cow cuddling is offered as part of half-day visits , and is part of an larger movement to connect people with country life. In the major urban center of Rotterdam, a newly opened floating dairy farm in the city’s oldest port invites city dwellers to visit the beasts.

About a decade earlier, in 2007, Mr. and Ms. Vullers — he a former supply chain manager, she a former accountant — traded their corporate lives to set up their farming shop in Naples, N.Y. (Population: 2,500. Claim to fame: a grape festival that takes place in the fall, with a competition for grape pie.) The idea of cow cuddling opened the barn gates.

In May of 2018, they purchased Bonnie and Bella, selecting them for their gentle personalities and lack of horns. “A lot of cows are not suited for it,” Mr. Vullers said. ”They can chase you out of the field.”