"TikTok we are trained professionals under supervision of the CEO of Auckland Transport who gave us his blessing and we are Red Bull athletes," they claimed.
When one commenter noted just how close the jumper had come to serious injury or death, they admitted the jump "was a bit scary".
The user was asked to post the full video, but claimed that TikTok would remove it if they did so.
A police spokesperson told the Herald they had no knowledge of the incident but said that "keeping our communities safe is one of our priorities".
"We are disappointed to see these types of dangerous acts as depicted in this video for the sake of a social media trend and would ask that this not be replicated," they added.
Auckland Transport spokesman Blake Crayton-Brown slammed the dangerous trend and warned that anyone taking part risked their life and put themselves in line for serious legal consequences.
"It's extremely disappointing to see another video glorifying idiotic and potentially deadly stunts involving Auckland buses doing the rounds on social media," Crayton-Brown said.
"This sort of behaviour is reckless, irresponsible and puts lives at risk, including passengers onboard, pedestrians and those in nearby vehicles.
"These stunts are also illegal, with the offence of endangering transport attracting penalties of up to 14 years imprisonment."
The video is the latest in a series of stunts that were recorded and shared online. Other videos have shown young Aucklanders climbing skyscrapers and cranes and hanging on to buses as they drive on major roads.
Auckland mayor Phil Goff said last year it was concerning the young people were putting themselves at risk and added they needed to consider the potential consequences of what they were doing.
"There have been deaths documented due to people doing stunts like this on social media and the last thing we want is a similar tragedy happening in Auckland.
"My message to anybody engaging in this sort of risky behaviour is to think of the terrible toll it would take on you, your family and friends if something goes wrong."