This morning on TVNZ's Breakfast, Ardern said it was made at 9pm, about an hour after the statements were released, and on the AM Show she said it was about two hours afterwards, which would have been about 10pm.
Bridges told reporters this morning that Ardern was muddying the waters.
"The Prime Minister this morning dribbling out little bits of information, it's still clear as mud about just what happened, who knew what, exactly when.
"Their first response was to go big and hard on a false allegation and to call in the police. They very shortly after that learned that wasn't right, and they sat on that lie."
Bridges has called for Robertson and Makhlouf to resign for implying that National had hacked the Treasury in spite of advice that there was no hacking.
Robertson has said he was only acting on advice from the Treasury, and Makhlouf said he made no link between the Treasury website being compromised and the National Party.
Bridges said even if their statements were released before the GCSB phone call, Ministers still did not release the GCSB advice after they were told about it.
Police advice that nothing illegal had happened was eventually released on the morning of Budget day, about 33 hours after Makhlouf's "hacking" statement had come out.
"Because GCSB told them otherwise, that it was a very different picture, the difference between criminal and not criminal, they sat on a lie," Bridges said.
"Jacinda Ardern, Grant Robertson, Andrew Little - at least those three knew all of the facts by then and they didn't come clean.
"If they don't have something to cover-up, let's see them come clean. Just tell us what happened, when, with no mucking around."
He stood by his call for Robertson to resign.
"No matter how you sugar-coat this, he was involved, he did sit on a lie ... Ultimately Mr Robertson is the Minister responsible for Treasury."
Ardern has defended not releasing the GCSB advice by saying there was a police investigation going on, and while ministers were aware of the GCSB advice, the full picture of what had happened was yet to emerge.
She said there was a dispute about the language used and, after becoming aware of the GCSB advice, ministers referred to the matter as "unauthorised access".
Ardern said the National Party could have cleared up the matter by saying earlier how they had obtained confidential Budget 2019 information, but Bridges said the onus was on the Government to front up because they were the ones who had claimed it was systematic hacking.
The State Services Commission investigation into whether Makhlouf misled the Government aims to be complete before the Treasury Secretary leaves on June 27 to take up a position as head of the Irish Central Bank.
He is being farewelled at a function in the Beehive on Thursday, but Bridges said he will not attend.
"Having called for his resignation, I don't think it's appropriate.
"I'm not going to sit there eating the canapes, given the position we're in and the need for real answer from him, from his minister, from the Prime Minister."