Witnesses said they felt “lucky to be alive” after the vehicle’s windows were shattered as it travelled between Deodoro venues to the main Olympic park on Tuesday night.
Three of the 12 passengers on board suffered minor cuts from flying shards of glass but no one was seriously injured.
David Davies, a Press Association photographer, said he was sitting at the back of the bus.
“There was a popping, cracking noise,” he added. "The bus didn't come to a stop but paused. Everyone was on the floor so I got on the floor as well.
“The bus driver stopped the bus about half a minute afterwards. People started shouting, 'Just keep going'. After a couple of minutes we had a police escort.”
The bus pulled over on the motorway shortly afterwards, with the driver speaking to police before it continued its journey.
Olympic officials have not confirmed what caused the windows to smash, saying stones might be responsible, but witnesses insisted they saw gunfire.
"We were shot at. I mean we could hear the report of the gun," said Sherryl "Lee" Michaelson, a retired US Air Force captain working for a basketball publication in Rio.
"We were on the highway going fast and we heard a loud noise and we just got shot at,” an Olympic volunteer who was on board told Reuters.
"Two windows and we could see the bullet. I guess we’re all lucky to be alive now.”
A photograph taken by a passenger showed a small hole, about the width of a finger, in one of the windows.
A spokesperson for the Rio organising committee, Mario Andrada, said forensic investigators were trying to determine if the projectile was a bullet or a rock.
"We haven't yet been able to confirm what kind of projectile hit the bus," he said. "We don't want to speculate."
It had been travelling between Rio's Deodoro zone, which is hosting events including hockey, basketball and rugby, and the press centre in the Olympic Park at around 7.30pm local time (11.30pm BST) on Tuesday.
The reported shooting occurred in the Curicaca district, just a few miles north of the city’s main venues.
The International Olympic Committee (IOC) said the incident was being investigated by security services and that it could not comment further until the “objects” had been identified.
Violent street crime in Rio de Janeiro raised security concerns in the run-up to the Games, with 85,000 soldiers and police deployed - twice as many as London did four years ago.
Thursday’s incident came after a bullet was shot through the roof of a tent where journalists were covering equestrian events on Saturday.
No one was injured and officials said it was suspected to have been fired by a gang member trying to shoot down a police blimp or drone.
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