Likely to be named Bush's national security adviser, the Stanford University administrator met with the Texas governor Wednesday.
After receiving his second regular intelligence briefing from the CIA, Bush sat alongside Rice in the living room of the governor's mansion and warned would-be international adversaries not to see this period of election uncertainty as an opportunity to attack U.S. interests abroad.
Rice later in the day got a second, more extensive briefing alone from the two CIA briefers. She retains her top security clearance from her national security job in the administration of Bush's father.
With the incoming Congress to be near-evenly divided among Republicans and Democrats, Bush said it was "a very unique moment in American history to promote a foreign policy that is bipartisan."
The meeting with Rice was the latest session intended to portray him as busy forming a new government and to showcase its would-be leading members. Bush met last week with retired Gen. Colin Powell, his near-certain choice as secretary of state.
There had been plans to announce White House staff selections this week, before potential Cabinet nominees, but Bush's advisers feared they would have looked overly confident had they done so during continued legal wrangling over the election. Announcements are now expected next week.
Bush indicated he was further along in picking a White House staff.
"When it comes to a White House staff, I've pretty well made up my mind on who should serve," Bush told reporters. "I've spoken fairly directly to people about possible service in the White House."
He said he is optimistic that court battles over the unsettled presidential election may soon be over. "I hope we can get this over with quickly. There's a lot of work to be done," Bush said.
Also Wednesday, an Alabama congressman introduced legislation to pressure a federal agency to release money and office space for Bush's transition team to prepare for a Bush presidency.
Republican Spencer Bachus wants to convince the General Services Administration that Bush should not be denied privileges afforded most presidents-elect merely because his opponent has contested the election results.
"I'm trying to send a message to GSA that if they fail to act tomorrow or the next day, we hold this legislation over their head," Bachus said. "They're handicapping George Bush's ability to be ready on day one."
The General Services Administration is given the authority to release transition funds under the Presidential Transition Act, passed in 1963 and updated in 1988. Under the bill, GSA must "ascertain the apparent winner" before awarding the funds and office space.
GSA spokeswoman Beth Newburger said Wednesday no winner is apparent yet, which is why the agency has denied Bush the transition privileges.
"We're following the law," Newburger said. "When it's apparent to everyone, it will be apparent to us."
Bachus' legislation would grant transition spoils to a candidate with victories certified by enough states to win a majority in the Electoral College. In addition, it would reimburse the Bush campaign for private funds it has raised to establish a transition office in a Washington suburb.
Bachus says even if Gore wins his appeals and becomes the next president, he already has the Washington office space necessary to build a new administration. Along with his vice president's mansion and office at the Old Executive Office Building, Gore has space in the West Wing of the White House.