All were taken to Kentucky River Medical Center in Jackson. No one was seriously hurt, and a hospital spokesman said everyone had been treated and discharged by midday.
It was raining lightly, foggy and dark when the bus, driven by Jesse N. Phillips, 21, dropped off the shoulder of the road and overturned, landing upright.
The children were on their way to Campton Elementary School, Wolfe Middle School and Wolfe High School when the crash occurred at 6:35 a.m. on Proffitt Fork Road.
The road runs off Ky. 15 about 3 miles southeast of Campton.
Russell Halsey, principal of the elementary school and spokesman for the school district, said the older children and the driver helped evacuate the students, and the crash site was relatively orderly.
"I was extremely proud of the students," he said. "We're thankful everyone's OK."
The most serious injury was a broken collarbone suffered by the bus monitor, Norma Hileman, 56.
It was not clear whether the terrain or weather might have helped cause the crash. Kentucky State Police were continuing to investigate yesterday.
The district's bus drivers have not filed any formal complaints about the road being hazardous, Halsey said.
It had rained heavily over-night in Wolfe County. High water from the storm closed schools in Montgomery and Powell counties yesterday.
Four of the six lanes of Interstate 64 in Clark County also were closed because mud had clogged drainage pipes, said Sgt. Brian Caudill of the Clark Sheriff's Department.
Traffic was limited to one lane in each direction from about 2:30 a.m. to 11 a.m.
