Speaking to the Herald afterwards, Bush said the police and prosecutors involved in the case had done exemplary work.
"The prosecution team, both the police and the Crown, have done Grace and her family proud in terms of how they went about this.
"It was all about Grace and her family. The team have conducted themselves so professionally, and it's an example of what we need to be in these circumstances."
Police Minister Stuart Nash said it had been a challenging investigation for police.
"I'm immensely proud of Detective Inspector Scott Beard and his whole team, both frontline investigators and the Police employees who work behind the scenes.
"This has been a difficult and distressing investigation. Police are human like the rest of us, and this investigation has been under trying circumstances. They have been absolutely professional and diligent throughout.
"My sympathies are with David and Gill Millane, her wider family and friends."
From the outset of the investigation, Beard had told his team that they were working for Grace.
She had gone missing in Auckland during her OE in December 2018, and the day after she was reported missing, Beard was called in to oversee the investigation.
"One thing you want is a photo of Grace up there," he told his team. "Because that's who we're working for. We're working to find Grace.
"She's not just a name - she's a person. So I want as many photos of her up on the wall as possible, so we know why we're here."
Prime Minister Jacinda Ardern was unavailable for comment earlier today as she was meeting with Papua New Guinea Prime Minister James Marape.
But at the time of Millane's death, Ardern had reached out to the Millane family.
"I cannot imagine the grief of her family and what they would be experiencing and feeling right now," she said in December 2018.
"From the Kiwis I have spoken to, there is this overwhelming sense of hurt and shame that this has happened in our country, a place that prides itself on our hospitality, on our manaakitanga, especially those visiting our shores.
"On behalf of New Zealand, I want to apologise to Grace's family."
Justice Minister Andrew Little said it would be inappropriate to comment on judicial decisions.
"My thoughts are with the family in what has been a difficult and distressing case."