Waugh, 38, who has led Australia to the top of the world rankings, will be attending the New South Wales state team's 2003-04 season launch in Bowral, near Sydney.
A two-hour drive away in Canberra, Australian Prime Minister John Howard will be entertaining Bush at a barbecue at his residence, The Lodge, among the nation's leading business and political figures.
"Unfortunately, he's got other commitments," Waugh's manager Robert Joske told Melbourne's Herald Sun newspaper on Wednesday.
"We stand on protocol here, and unfortunately he had accepted the team commitment to be in Bowral. He would have really thoroughly enjoyed it, and he's quite disappointed he can't go."
Waugh is one of his country's most well-known figures and Howard, a self-confessed "cricket tragic", has joked in the past about which role is more prominent in Australian society, Test cricket captain or prime minister.
