Officers are appealing for help from members of the public to assist them in identifying the two men they would like to speak to in connection with the incident.
On Thursday 10th January at around 6pm, two men got on the number two bus that was travelling through Maltby.
They chatted to the driver when they first got on board and then sat down on the seats at the back of the bus.
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Around 10 minutes later, a 16-year-old boy got on the bus at Braithwell and sat down on seats that face each other.
A South Yorkshire Police spokesman said: “The two men are then believed to have covered their faces, headed toward the teenager and sat next to, and opposite him.”
“Over a 15 minute period, the men are alleged to have threatened violence and demanded money from the teenager.”
“One of the men is then believed to have threatened him with a knife.”
“The teenager then managed to alert the driver, who stopped the bus and the two men ran off,” she added.
Both of the men are described as being white and aged in their early 20s.
The first man has trimmed, mousy brown hair and is of a large build. He was wearing a beige hooded jacket.
The second man has cropped, blonde hair and is of a thin build. He was wearing a checked shirt with a white scarf or jumper around his neck.
Anyone who believes they may know the identity of either of the men, may have witnessed the incident or has any other information, should contact South Yorkshire Police on 101 quoting crime reference number C/3640/2013.
Alternatively, anyone with information can call Crimestoppers, anonymously, on 0800 555111 and leave a recorded message for investigating officers.
You can also leave information via a form the Crimestoppers website at http://www.crimestoppers-uk.org