The video, released by the Associated Press news agency almost six months after the storm devastated New Orleans, shows federal disaster officials warning Mr Bush and his homeland security chief in dramatic and sometimes agonising terms.
The president asked no questions during the final government-wide briefing, but assured soon-to-be battered state officials that "We are fully prepared".
Katrina struck on August 29, killing more than 1,300 people, many in New Orleans.
More than 2,000 people are still officially listed as missing.
Six days of footage and transcripts obtained by AP show in detail that while federal officials anticipated the disaster, they were fatally slow to realise they had failed to assign resources to deal with it.
Some of the footage conflicts with the defence that federal, state and local officials made in trying to deflect blame and minimise the political fallout.
The government's slow reaction to the devastation has contributed to a major slump in the Bush administration's popularity rating.
In the video, the then head of the Federal Emergency Management Agency (FEMA) Michael Brown said: "This is, to put it mildly, the big one".
He told the president and Homeland Security Secretary Michael Chertoff that he was concerned that there weren't enough disaster teams to help thousands of people stranded at the Superdome, saying it was "about 12 feet below sea level."
"I don't know whether the roof is designed to withstand a Cat Five hurricane," Mr Brown was heard saying in the video.
Head of the National Hurricane Centre, Max Mayfield, said during a briefing there was "very, very grave concern" that New Orleans' levees could be toppled by Katrina.
Four days after the hurricane hit, Mr Bush told a television interviewer that "I don't think anybody anticipated the breach of the levees".
The president listened to the August 28 briefing by video link from his Texas ranch where he was on holiday.
He asked no questions but did say: "I want to assure the folks at state level that we are fully prepared".