"If you happen to be walking around and run into the vice president, you might give him a few pointers," said President Bush, referring to the incident in which Cheney accidentally shot a companion while hunting in Texas.
President Bush, who said he'd be at West Point next month to deliver a commencement speech, honored twelve NCAA teams, including Stanford's women's cross country team, for winning national titles during the 2005 and 2006 seasons.
President Bush's quip about Cheney got the biggest laugh at the ceremony on the South Lawn.
The "Lady Terps" received the biggest applause.
The University of Maryland's women's basketball team won its first NCAA title on Tuesday, overcoming a 13-point deficit to force overtime and beat Duke University 78-75.
"Less than 48 hours ago, they were cutting down the nets in Boston," said President Bush. "Here they are soaking up the sun at the White House. We welcome you here. We marvel at your dramatic overtime win and we thank you for being such fantastic athletes."
The women's basketball team was one of three Terrapin teams Bush honored from the University of Maryland. The university's women's field hockey team and men's soccer team were NCAA champs in 2005.
"Perhaps one theme of Champions Day is 'Fear the Turtle,"' Bush said.
The Auburn University women's championship swimming and diving team gave the president a skimpy black bathing suit.
"Awfully thoughtful of you," he said, holding it up for the audience to see. "I'm not gonna wear it."
The other teams honored were the University of Colorado men's and women's skiing team, the University of Florida men's basketball team, the University of Wisconsin men's cross country team, the University of Portland women's soccer team, and the University of Washington women's volleyball team.