The boy, who police believe was aged between 13 and 17, was violent towards the bus driver on the number 1 First York Bus on Oak Tree Lane, Haxby, between 1.50pm and 2.06pm on June 16.
Officers say there were other passengers on the bus who witnessed his behaviour, but did not reveal any further details about what happened.
The boy is described as white, about 5ft 6ins tall, slim, with short brown curly hair.
He was wearing a black beanie hat with a white North Face logo on the front, black t-shirt and black tracksuit bottoms.
Anyone with information is urged to call police on 101, quoting reference number 12210140733.