Jason George O’Neil, 26, was behind the wheel of a Peugeot which crashed west of Carlisle on September 26 last year.
At the city’s crown court, O’Neil pleaded guilty to causing serious injury to Anthony Queen by dangerous driving.
The court heard O’Neil’s vehicle was exceeding the 40mph speed limit and had crossed double white lines, close to a bend at Micklethwaite, immediately before the collision.
This involved an oncoming bus containing passengers, some of whom were said to have been thrown from seats.
Defence lawyer John Smith said O’Neil, who also admitted a no insurance offence, believed he had been travelling at around 55mph before the crash.
Mr Smith acknowledged in court that the injured car passenger had been detained in hospital for more than a week.
However, medical evidence was still being sought to determine the precise nature of the injuries suffered.
The judge asked for background information on O’Neil, of Raffles Avenue, Raffles, Carlisle, who is set to be sentenced on June 24.
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