Bachmann, a Republican congresswoman from Minnesota fresh off a straw poll victory in Iowa, stayed on her campaign bus until Perry finished speaking at the GOP dinner Sunday at the Electric Park Ballroom on the grounds of the National Cattle Congress in Waterloo, The New York Times reported.
"Man, y'all got a crowd here -- this is awesome," the Texas governor said.
"You'd think you were in Texas if you didn't know better."
Perry later defended the Tea Party, saying the movement was not "angry."
"We're indignant at the arrogance and audacity this administration is showing about the values that are important to the people of America," he said. "We're indignant about a government that borrows trillions of dollars because they don't have the courage to say no."
During her speech, Bachmann made no acknowledgment of her rival, even though he sat at a table just feet from where she stood.
"The Tea Party has been the best antidote to the out-of-control spending we have seen," Bachmann said. "The Tea Party has done something else for us too. They pointed out the unbelievable level of debt we have."
Perry applauded politely when Bachmann criticized President Barack Obama, but otherwise sat quietly during her speech, the Times said.
When she concluded her speech, Perry quickly left the building without shaking her hand, the Los Angeles Times reported.
Bachmann campaign manager Ed Rollins told The New York Times afterward the lack of interchange between the candidates was OK because "the debate will be there" soon enough.
"We've got three to four debates in September," he said. "We will all be on the same stage, and everybody gets to make their judgments."
Perry later flew to Manchester, N.H., arriving at a picnic wearing brown boots, a Western-style belt and a checkered sport coat.
When asked by reporters if he might be "too Texas" for independent voters, Perry took the opportunity to separate himself from former President George W. Bush.
"We're not all carbon copies in Texas,'' he said. "We're a little bit different."
National front-runner Mitt Romney, a former governor of Massachusetts, planned to be in New Hampshire Monday and Tuesday, then fly to California, Wyoming, Idaho and Utah to raise campaign funds, campaign officials said.
Aides said he would avoid the back-and-forth of the Republican nominating contest and focus instead on Obama, criticizing the president's three-day Midwest bus tour.
Obama plans appearances in Minnesota, Iowa and Illinois, a region seen as vital to his re-election, to "discuss ways to grow the economy, strengthen the middle class and accelerate hiring in communities and towns across the nation," the White House said Sunday night.
He was expected to make a case he has stabilized the economy and has the right prescriptions for continued improvement.
Former Utah Gov. Jon Huntsman Jr., a former ambassador to China under Obama, increased his criticism of Romney Sunday, positioning himself as a Romney alternative in New Hampshire.
U.S. Rep. Ron Paul, R-Texas, who finished a close second to Bachmann in Iowa's Ames Straw Poll Saturday, could also influence the race with his libertarian views, which have increased in popularity in the current U.S. economic climate, The New York Times said.
Former Minnesota Gov. Tim Pawlenty quit the race Sunday after coming in a distant third in the straw poll.
He told ABC's "This Week" voters were "looking for something different" from what he offered as "a rational, established" two-term governor with a "strong record of results, based on experience governing."
Other Republicans said his low-key, guy-next-door image was no match for Bachmann's crowd-pleasing fire, the Los Angeles Times said.
Perry said he'd like Pawlenty's endorsement but the Minnesotan said he wasn't ready to throw his support to another candidate.