Peter Colquhoun, 28, planned the trip of pupils from Lanark Grammar to Alton Towers theme park, Staffordshire, in 2010.
The coach carrying 39 pupils, three staff, and two adult helpers, crashed in a snowstorm and killed Natasha Paton, 17, from Cleghorn Village, near Lanark.
The first day of a Fatal Accident Inquiry into Natasha's death heard Mr Colquhoun, a physics teacher, describe the moments before the smash on the A73 near Biggar, Lanarkshire.
Giving evidence at Lanark Sheriff Court, he told how the trip on March 31, 2010, turned to horror.
He said: "As we were going down the slope I saw the wall of the bridge approaching and I knew something wasn't quite right. I remember the driver trying to turn his wheel to the left quite frantically, but it wasn't turning enough.
"Then we hit the wall of the bridge and it fell on its right hand side into the river.
"My head was under the water. There was obviously hysteria and people were screaming.
"I got to the surface and I was able to stand and look around to see what had happened."
Mr Colquhoun said he and a colleague smashed open the front window in an attempt to rescue trapped pupils and staff.
He helped the driver, who had said he thought his leg was broken, out of the water and on to the banking.
Mr Colquhoun, who suffered a cut arm and a head wound, said: "My concern was getting the pupils out of the bus. Some of the lads at the back had got the rear skyhatch open and were getting people out that way.
"When I was down at the front I was trying to feel around under the water as best I could, but it was so cold I couldn't tell what things were."
He said he only became aware a pupil was missing and had died when he was discharged from hospital later that day.
The inquiry continues.