The former White House adviser made the remarks following Mr Bush’s speech in New York earlier this week, in which he denounced bigotry in Trump-era American politics and warned that the rise of “nativism” had clouded the nation’s true identity.
Mr Bannon told the California Republican Party convention Mr Bush had embarrassed himself and did not know what he was talking about.
The chairman of right-wing news websiteBreitbart,said Mr Bush has no idea whether “he is coming or going, just like it was when he was president”.
The remarks came during a speech thick with attacks on the Washington status quo, echoing his call for an “open revolt” against establishment Republicans.
“There has not been a more destructive presidency than George Bush’s,” Mr Bannon added, as boos could be heard in the crowd at the mention of the former president’s name.
Mr Bannon also called the “permanent political class” one of the great dangers faced by the country.
Mr Bannon also took aim at Silicon Valley and its “lords of technology”, predicting that tech leaders and progressives in the state would try to secede from the union in 10 to 15 years.
He called the threat to break up the nation a “living problem”.
Mr Bannon also tried to cheer long-suffering California Republicans in a state that Donald Trump lost by more than four million votes and where Republicans have become largely irrelevant in state politics.
In Orange County, where the convention was held, several Republican House members are trying to hold onto their seats in districts carried by Hillary Clinton in the 2016 presidential contest.
“You’ve got everything you need to win,” he told them.
Mr Bannon ended his speech to a standing ovation. But not all Republicans were glad to see him.
In a series of tweets last week, former state Assembly Republican leader Chad Mayes said he was shocked by the decision to have the conservative firebrand headline the event.
“It’s a huge step backward and demonstrates that the party remains tone deaf,” Mr Mayes tweeted.
Additional reporting by PA