Two windows were smashed and three of the 12 people on board suffered cuts when the bus was travelling between the Deodoro hockey venue, north of Rio, and the main press centre at Barra da Tijuca, southwest in the city.
Mario Andrada, chief spokesman for Rio 2016's organising committee, said, "We don't know yet if the bus was shot, or it was a stone."
Lee Michaelson, a reporter on women's basketball and a former US Air Force captain, said, "I know what a gun sounds like. With my background and training, I got down on the floor as much as I could and I hollered to the others to get down.
"The others were just beginning to respond. I started yelling at them, 'Get down, get down, we are taking fire'."
The International Olympic Committee (IOC) said security forces are investigating the incident.
"There was a popping, cracking noise. There were pierced holes in the glass when it happened. Everyone was on the floor so I got on the floor as well," added an unnamed photographer from the UK's Press Association.
"The two windows did not shatter immediately but one of them shattered as we drove along the motorway," the photographer added.
A police escort quickly arrived and accompanied the bus back to the press centre.
A statement from the Games organising committee said military patrols would be "increased" in response.
On Saturday a bullet pierced the roof of the media tent at the Olympic Equestrian Centre - which is located near a military compound. The competition was not disrupted and nobody was hurt.
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