A 5-year-old girl and the driver were killed and two other students were critically injured, authorities said.
The crash happened just before sunrise after rain showers had moved through the area, but authorities didn't know what caused the bus to crash into the concrete pillar in the middle of a city street. They were awaiting autopsy results on the 60-year-old driver.
Mitch Gibboney said he was on his way to work at a nearby trucking company around 7:45 a.m. Monday when he saw smoke coming from under the bridge. Because it was dark, he didn't realize until he got there that the smoke was coming from the bus.
Gibboney helped lead some children out a side door near the middle of the bus. Other passers-by also rushed to help.
"They were shaken up and bruised and a little bit bleeding. Some of them were crying," Gibboney said. "I saw a couple holding their arms and wrists and a couple of them had bloody noses where they probably hit the seat in front of them."
The bus was carrying 50 students to Indianapolis Lighthouse Charter School on the city's east side, city fire Capt. Rita Burris said. The impact tore apart the front end of the bus, smashing in the first several feet of the driver's side.
Police identified the girl killed as Donasty Smith and the driver as Thomas Spencer II, 60, of Indianapolis. Two male students were critically injured and were taken to Indianapolis hospitals along with eight others whom Burris characterized as "walking wounded."
Burris said fire department crews spent about 45 minutes extricating four trapped people, including a student who was tangled inside a wheel well.
The students ranged in age from 5 to 16, Burris said. Uninjured students were taken to the school -- which has about 650 students from kindergarten through high school -- about two miles away.
The driver of another school bus that was behind the one that hit the bridge and an approaching car told investigators the bus wasn't speeding in the 35 mph zone, police spokesman Anthony Schneider said.
"Boom! It just hit," Schneider said. "They didn't see anything like the bus swerving."
Tami Presley told WISH-TV she was on her way to work when she came upon the crash scene.
"I couldn't figure out what it was that was under the bridge," Presley said. "As I was pulling under I just see kids just start jumping off. They were all screaming and crying."
She said she tried to console the children and that a paramedic on board the bus was trying to help the injured.
Kevin Mays, who works at the nearby CSX Transportation rail yard, said he walked over to the scene about five minutes after the crash. The bus was so crumpled that he expected to see terrible injuries.
"There was a lot of chaos and crying from the kids," Mays said.
Lighthouse student Dimitri Smith, 15, missed the bus and was riding to school with his grandfather when he saw the accident scene.
Smith told The Indianapolis Star the bus driver was "a really cool guy."
"He wanted all of us to be safe, and he was a good bus driver," he said.
The bus is owned by Miller Transportation. A woman answering the phone at the company's Indianapolis office said it would have no comment.
Federal transportation records show Miller Transportation had one crash involving a death in the past two years, but it was unclear whether that involved a school bus. The Louisville, Ky.-based company also operates charter and tour buses.
Beth Bray, who works for the Indianapolis mayor's office and was helping to answer the telephone at the school Monday, said the school had no comment on the crash Monday.
"We're trying to help parents and get everybody coordinated," she said.
The school dismissed its students at midday, several hours earlier than normal.
Also Monday, a school bus in Washington state overturned on a highway, injuring dozens of students, including three seriously. The bus veered off the road, overcorrected and rolled on Highway 281 just south of Quincy, an agricultural region about 120 miles east of Seattle, said Lt. Scott Martin of the Washington State Patrol.
Martin said the cause was under investigation. Roads were bare and dry when that bus rolled.