The victims two Seward High School students and the mother of a band member died at the scene, Douglas County Sheriff Tim Dunning said.
"On top of everything else that's taken place it's terrible," Dunning said. "The worst accident I've seen in my career. Without a doubt."
The bus, which was traveling on U.S. 6, was on its side as rescue workers tried to pull passengers out.
Seven people, including two students, were in critical condition. Two others were listed as serious and one fair.
Methodist Hospital spokesman Ed Rider said they had treated four students two complained of back and neck injuries.
Authorities weren't sure what caused the bus to stray off course but don't believe another vehicle was involved. The road curves just before the bridge, which is about 40 feet above a small stream.
"The bus started shaking. People started screaming," said band member Ryan Tremblay, who was in the back of the bus. "The bus started to lose control."
Tremblay was bleeding from a cut on his right ear. He was treated in an emergency triage area set up near the accident site.
There were 31 people on the bus, which was the first of three taking the Seward High School band members back to Seward, about 60 miles southwest of Omaha.
Students who were on the other buses returning from the competition were sent to a school about 10 miles away from the accident site, where they waited to be picked up by their parents.
"They don't want to put anybody else on a bus in light of the tragedy," Police chaplain R.D. Terry said.
By AMY LORENTZEN
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