The impact from the car caused the bus to plunge off a highway overpass.
Witnesses say that car came up on a side lane and apparently hit the bus. Both vehicles were on their way to a downtown technical center, where students can receive special science and math credits.
Gary Van Etten, the investigator in charge of the probe for the NTSB, said late Monday that there may have been a malfunction in the steering system of the car. The car's driver told investigators "he was having problems steering the car and they got progressively worse when he lost control of the car," Van Etten said.
"As of yet we have not found anything that is any severe violations or defects in the way of the operations," Van Etten said
Several people who witnessed the event said the car, a Toyota Celica, appeared to have steering problems, Huntsville Police Chief Rex Reynolds told CBS affiliate WHNT-TV in Huntsville.
"There was no deliberate erratic driving on part of the driver of the Celica prior to the accident," said Reynolds. Police said the 17-year-old driver of the car has received death threats since the crash.
The investigation also revealed that the bus driver likely was not wearing a seat belt. The NTSB believes the driver was ejected through the bus loading door before it went over the edge of the overpass. Investigators are waiting for the bus driver's medical condition to improve before they interview him, WHNT-TV reports.
Anthony Scott, the bus driver, remained hospitalized Monday, along with two student passengers, hospital officials said.
Also Monday, parents, teachers and students, some on crutches, limping or with cuts and bruises, attended the funeral Monday for a 17-year-old girl who was among the four Lee High School students killed last week.
Thousands went to the funerals of Crystalle Renee McCrary's schoolmates during the holiday weekend as people in the school and community struggled to deal with the fatal crash.
Nicole Sharika Ford, 19, was buried Friday. Tanesha Estella Hill, 17, and Christine Collier, 16, were laid to rest Saturday.
Two of the girls died at the scene, and two others died later. Forty students were aboard the bus when it plunged about 30 feet and crashed nose-first onto a street.
Huntsville schools observed a moment of silence at 10:10 a.m., the moment of the Nov. 20 crash.
At Lee High School, principal Brenda Chunn read the girls' names and rang a bell after each, city schools spokesman Keith Ward said.
"There were a few tears, but it was a very solemn, very somber moment," he said.
Ward said officials will spend this week trying to get back into a normal routine while still acknowledging students' grief.
The tech classes will resume Tuesday, Ward said. Students now will be bused to the center using a route that doesn't include taking I-565, but will still be allowed to drive their own cars to the center, he said.
Ward said grief counselors would be at the campus "just as long as they need to be."
A nonprofit charitable organization delivered 900 teddy bears to students Monday.
"After they were passed out ... every student was carrying around a teddy bear," Ward said. "It sounds like a very simple gesture, but sometimes the simple gestures mean a lot."