It intends to sell a package of weapons, including precision-guided bombs, to the Saudis as part of US strategy to bolster the defences of Arab allies against threats from Iran.
The US president, who flew to Riyadh from Dubai on his eight-day Middle East trip, was granted the privilege of staying King Abdullah's home.
The king greeted Mr Bush at the base of the steps of Air Force One. A band played each country's national anthem as the leaders walked on a red carpet behind a high-stepping uniformed officer carrying a gold sword. In the airport terminal, the president shook hands with a long procession of officials and military officers.
Earlier, in Dubai, Mr Bush got a flavour of the cosmopolitan banking and business hub, whose glass skyscrapers and booming construction have turned it into the capital of Middle East bustle.
The soaring Arabian Gulf city-state was his second stop in the seven-state United Arab Emirates federation, following his lecture in Abu Dhabi and an opulent picnic at a desert horse camp on Sunday.
On a day of cultural diplomacy, Mr Bush began with a stop at the historic home of the former ruler of Dubai, now a museum loaded with photos and artefacts of the emirate's history.
Mr Bush then had lunch with students of the Dubai School of Government, a research and teaching institution that focuses on public policy in the Arab world.
US agrees Dh71.8bn Saudi arms package