South Yorkshire Police said the 15-year-old boy had been hurt while running along Eastern Avenue yesterday morning.
A spokesman said: “The boy is currently in hospital in a serious but stable condition after being involved in a collision with a single-decker bus.
“No-one else was injured during the incident.”
The bus had been travelling towards the city centre prior to the collision, which was reported at around 10.30am.
Officers investigating the collision are still keen to speak to anyone who saw what happened.
Call 101, quoting incident number 351 of 6 May 2017, to pass on information.