Bush met leaders of the new Democrat-controlled Senate.
A day after having lunch with top House Democrat Nancy Pelosi, Mr Bush held talks with her Senate counterpart Harry Reid and senior Democratic Senator Dick Durbin.
The men will control the upper chamber when the new Congress convenes in January.
Democrats are flexing their new muscle after their election win which gave them control of both the House of Representatives and the Senate for the first time since 1994.
"There is a great opportunity for us to show the country that Republicans and Democrats are equally as patriotic and equally as concerned about the future and we can work together," Mr Bush said as he met the senators.
Mr Bush, who makes his home in Texas, also had warm words for Mr Reid, also from a western state, Nevada.
"We tend to speak the same language, pretty plain-spoken people, so (that) should bode well for our relationship," he said, publicly turning the page after a bruising midterm election campaign.
Mr Reid said the discussion had been excellent. "We've talked about issues that are important to our country. (The) election's over," he said.
Both sides have put on a show of cooperation to appease voters angry at the bitter divisions in US politics, but wrangles, notably over Iraq, were already breaking out.
Senior Democratic Congressman John Murtha warned that Mr Bush's decision to part with Defence Secretary Donald Rumsfeld was not enough to smooth over differences on the war.
"All right, you fired the secretary of defence. But that's not a change in policy," Murtha said on CNN.
"What we have to do is give a deadline to the Iraqis," Murtha said, adding that he favored opening an investigation into how Bush's White House entered and managed the war in Iraq.
Roy Blunt, House majority whip for the Republicans, accused the Democrats of wanting to simply pull out of Iraq.
"We clearly have to be sure we take the war on terrorism and the war on Islamic totalitarianism seriously. You can't naively assume that this is going to end if we just decide to stop fighting," Mr Blunt said on Fox News.
"I think the American people in the next two years are going to see, be reminded of what the Democrats are truly for."
Democrats have demanded modifications to US policy in Iraq, where violence is raging three years after the US invasion.
Eyes in Washington were also turning to a bipartisan commission probing new approaches to the occupation of Iraq, after Bush admitted voters were fed up with the situation in a country where 2,800 US troops and tens of thousands of civilians have died.
The group co-led by former secretary of state James Baker, due to report within months, is seen by many observers as a chance for both parties to coalesce around a common strategy.
White House spokesman Tony Snow said Mr Bush would meet members of the group at the White House on Monday, and said senior officials, including Mr Rumsfeld and Secretary of State Condoleezza Rice, would also be briefed.
On Thursday, Snow said Bush would not necessarily adopt the group's recommendations.
"To the extent that the Iraq Study Group has fresh ideas and analysis that we think is going to be interesting and helpful, we're going to be grateful for it," Mr Snow said.
"But the idea that somebody says, 'Ah-ha, here's the document, let us follow' -- no, it doesn't work that way."
In another political brushfire, the White House resubmitted the nomination of hawkish UN ambassador John Bolton to the Senate, sparking an immediate row with Democrats.
Mr Bolton had previously been blocked by Democrats together with a rebel Republican in 2005, but was then granted a recess appointment by Mr Bush.
The White House's move appeared to be a bid to get Mr Bolton approved in a "lame duck" session of Congress still controlled by Republicans which opens next week.
Democratic Senator Chris Dodd reacted angrily, accusing the White House of trying to "jam this nomination through."