She says Sir Peter came out and approached them and began making conversation.
Bridger said Sir Peter had warned the group not to drink and drive before going on to say they must not be local.
"I go 'Yeah, I'm actually born here'. That's when he said 'Well this is a white man's island and you should acknowledge that'," she said.
Sir Peter, in a press statement, said he was "extremely disappointed that a young woman on Waiheke Island had misinterpreted some light-hearted banter he had with her".
"I was joking with her group about not drinking too much because there were lots of police on the island. She said that she was Tangata Whenua and could do what she liked, and I responded with a joke about it being a white man's island also.
"This was not a serious comment and was only ever intended to be light-hearted banter.
"When she later informed me she was offended by my comment I apologised unreservedly. There is no way I can ever be accused of being rascist.
"The irony is that I was with my own granddaughter, who is herself of Ngapuhi heritage."
Leitch's Facebook page was flooded with angry posts from members of the public after Bridger posted the video.
Bridger's mother, Sarndra Wharepapa, earlier told the Herald she had got up and went inside to speak to him after "a good five minutes" of mulling over what he'd said.
"I just said to him 'I really think what you've just said to my daughter is unacceptable. I'm quite offended that you could talk to my daughters like that'."
Bridger was upset and tearful over the incident, saying it was the first time she had experienced anything like it.
She said he did not offer an apology or try to explain why he made the comment.
The group said the manager approached them after the incident and offered them a free wine tasting tour as compensation.
Numerous comments have now been posted onto Sir Peter's Facebook page. Some are asking for his version of events. Others are telling him he should be ashamed.
Bridger's video was widely shared before it was removed, and had received more than 90,000 views.
In the post explaining she had deleted the video, she said her "point was made".
"I was just upset that someone whom I once looked up to had that mentality."
"People were going a bit overboard with threats and racist comments but that's not me, I don't wish any bad upon anyone and making more racist comments will make us no better.
"I don't like attention, that's not me, but the video went viral and backlash happened. I will contact him myself and hopefully he'll understand why I was so upset . . . Waiheke is a beautiful place everyone should be able to enjoy."
