Public representatives and trade union Siptu are calling for action to ensure bus surfing does not become a trend.
It comes after a video was circulated on social media of a young person clinging to the back of a Dublin Bus 40C travelling at speed on a main road near Finglas.
Dublin Bus said yesterday it was investigating the incident.
Siptu's transport sector organiser John Murray called for an information campaign to be launched to warn of the dangers of this kind of behaviour.
"I think it's absolutely shocking to see someone doing something like that," he said.
"It's hard to see from the video, but it seems to be a young person showing blatant disregard for their own safety.
"Think of the bus driver in this situation if a young person was knocked down or, God forbid, killed doing this. That driver is not going to be put in a good position."
Labour councillor and former Dublin Lord Mayor Brendan Carr said of the video: "This is incredibly reckless and shows a complete disregard for himself and other road users.
"He could have fallen off and killed himself or fallen off and been hit by a motorist.
"I hope this does not develop into a trend we start to see on the streets, and I would ask the gardai to stamp this out immediately.
"Hopefully someone can help identify who this person was."
Fianna Fail councillor Paul McAuliffe described the incident as "utter stupidity".
"The prospect of services being affected as a result of this behaviour, particularly if it continues, will be a concern for local commuters that rely on the bus on a daily basis," he said.
Last year, a young girl who sustained a severe brain injury after she fell off the side of a Luas tram in Dublin while "tram surfing" settled a High Court action for more than €500,000.
Rebecca Kelly was 13 when she and a friend jumped onto the outside of a Luas tram, gripping on to the edge of the doors as it departed the Fatima station on the Red Line.
She fell back on to the tracks, striking her head against them, and had to be rescued by her friend.