The military says the vast majority of American military personnel who have passed through since 2016 have stayed at other area hotels, not Mr. Trump’s. On Thursday, the Air Force said in a statement that it had found 659 instances when its flight crews stayed overnight in the area in the past four years. Of those stays, the Air Force estimated that 6 percent, or about 40 — far more than had previously been identified publicly — went to Mr. Trump’s property. Trump Turnberry was closed for renovations from 2015 until mid-2016.

Those who did stay there paid a discounted rate of as little as $130 a night, compared to a typical price of about $380 a night.

“To me, it was honestly just a hotel, a place to sleep,” said Nathan Wendzel, 33, a helicopter pilot, who spent a night at the Trump Turnberry last September, along with about 35 other members of his Iowa National Guard unit, on their way back to the United States from a trip to Kosovo. “It is better than a tent with no air conditioning.”

Neither Mr. Trump’s company nor the United States military has disclosed how much government money has been spent at the Trump resort. But a dozen Trump Turnberry staff members, all speaking on condition of anonymity for fear of reprisals, said the military stays have been a regular occurrence and, often, encompass surprisingly large groups.

Buses like the one that arrived in July periodically turn up at midnight or 2 a.m. carrying dozens of soldiers or Marines, several hotel staff members said. Less expensive hotels, like a TraveLodge and a Premier Inn, are next to the airport — the Trump Turnberry resort is about a 40-minute drive.

The bookings for United States military personnel staying at the Trump resort are made by employees of the Glasgow Prestwick Airport, which has an incentive to curry favor with Mr. Trump. The airport has become economically reliant on the military refueling flights, creating at least the appearance of a motive to steer business to the American commander in chief.