They were remanded in custody for a trial at the High Court in Greymouth on May 23 next year.
They are accused of murdering Mr Bambrough, 54, in Westport on October 12, 1999, and burying his body in a shallow grave at Denniston, about 30km north of Westport.
It is alleged Wilding's car was used to carry the body before being torched in Nelson a couple of days later.
Mr Bambrough's body was not found until September 22 this year.
Today Wilding admitted a joint charge (his brother Devon and Brian McCormack are co-defendants) of wilfully setting fire to the car.
On that charge he was remanded in custody for sentencing in the High Court on February 15.
Wilding and McKenzie are alleged to have murdered Mr Bambrough by throttling him and holding his head under water in the Buller River.
McKenzie has since admitted being present when Wilding allegedly committed the murder and helping in the disposal of the body. He led police to the grave at Denniston.
A Nelson man said Wilding told him in late 1999 he had committed a murder, describing how he strangled a man.
A few weeks later on a trip to Westport, Wilding allegedly said: "I know this road. Last time I came down this way I had something in the boot."
The witness and Wilding travelled to Upper Hutt together in 2000 each intending to enrol in polytech courses.
In March 2000 Wilding again mentioned the murder and said he would not mind killing again. The alleged target was a man named "Chesty".
Asked if he was worried the body would be found, Wilding allegedly said: "No. It won't be." Under cross examination the witness admitted phoning Nelson police telling a detective on January 4, 2000, that Wilding had confessed to a murder.
The witness said this was insurance in case something happened to him while he and Wilding were living in Upper Hutt.
He was "shit scared" of Wilding but still agreed to shift to Wellington with him.
The witness denied the reasons for accompanying Wilding was to spy on him for police but admitted the detective had asked him to take a note of any more references to the killing.
The witness also admitted Wilding at one stage laughed and said: "The cops are f*** wits. It (the murderer) is not me. I know something about it but it's not me. It's a nutter from Westport."
Wayne "Stetch" Shearer was one of the last to see Mr Bambrough alive.
He said he "gave him a couple of open handed clips around the lug hole" (ears), because he had uttered sexual remarks about children at a party at McKenzie's mother's house.
Mr Shearer had not met Wilding or McKenzie before, but at about 11.30pm he accepted a ride home from the two accused, leaving Mr Bambrough sitting on a sofa.
He said he knew nothing about his disappearance until McKenzie's mother arrived at his home at 4.30pm the following day asking if he knew where Mr Bambrough was.