It happened outside St Aiden’s High School on Oatlands Drive at around 8.50am on Monday 1 July 2019.
The cyclist, a boy from Harrogate, was taken to Leeds General Infirmary where he remains in a serious but stable condition.
Police are appealing to anyone who was in the area on Monday morning and saw the cyclist or the bus prior to the incident and to anyone who saw the collision itself, to contact them.
They would also like to hear from anyone with dash-cam footage of the incident or the moments before it happened.
Anyone with any information is asked to contact Traffic Constable Julie Brown of North Yorkshire Police’s Road Policing Group quoting reference number 12190118390.
The occupants of the coach were uninjured.