The collision occurred in Llanfair Caereinion on Monday afternoon on School Lane off Neudd Lane.
The bus driver and four children went to hospital, with three children being airlifted and the fourth taken by road, along with the bus driver. A fifth child was discharged at the scene.
Sergeant Robert Hamer, from Dyfed-Powys Police's Roads Policing Unit, said: “The incident happened as school was finishing for the day and there were a lot of people picking up children at the time.
"We have already spoken to a number of witnesses and we are now asking that anyone else who was in the vicinity of the primary and secondary schools on Neuadd Lane, and may have witnessed the incident, to get in touch.
"We would especially appeal to anyone who was parked in the area, and may have dash-cam recordings of the incident, to contact us."
Montgomeryshire MP Craig Williams, also raised the horrifying incident in the House of Commons during Prime Minister's Questions.
There has been no official confirmation of the condition of those injured in the incident, but Mr Williams told the House of Commons that "everyone is in a stable condition".
He said: "On Monday at 3.25pm a school bus crashed into a group of school children in Llanfair Caereinion. Three children were airlifted to hospital with another child and a bus driver taken by ambulance and a fifth child discharged at the scene.
"Everyone is in a stable condition. Clearly this is a tragic accident that will stay with the community for some time."
Anyone with information that could help officers is asked to report it to Dyfed-Powys Police, either online, by emailing firstname.lastname@example.org, or by calling 101. If you are deaf, hard of hearing, or speech impaired text the non-emergency number on 07811 311 908. Quote reference: DP-20220523-232.