He said the financial meltdown had created hardship for many Americans, but pledged : "We have been through tough times before and we're going to come through this again."
Mr Bush said the rescue plan would free up credit for businesses and families but that it would take some time to work.
"Thawing the freeze in the financial system is not going to happen overnight," he warned.
The US president was speaking at an office supply company outside Washington, following talks earlier with European leaders earlier on Tuesday.
Gloomy Bernanke
Meanwhile governments around the world have taken more steps to try to ease the credit crisis:
European Union finance ministers agreed to increase the guarantee for bank savings accounts to at least 50,000 euros ($68,250; £38,900)
The Netherlands, Spain, and Belgium announced they would protect savers' deposits of up to 100,000 euros (£77,700; $136,776)
Taiwan said that it would fully protect depositors' savings should a bank fail
The US Federal Reserve announced plans to buy massive amounts of short-term debt from companies in an effort to unfreeze the money markets
The Icelandic government took control of the country's second biggest bank
Australia's central bank lowered interest rates from 7% to 6%
On Tuesday the Dow Jones Industrial average ended more than 500 points lower at 9447.
Earlier London's FTSE 100 index closed up slightly despite heavy losses by banking shares. France's Cac 40 index also ended higher.
Meanwhile the chairman of the US Federal Reserve, Ben Bernanke, made a gloomy assessment of the financial crisis.
"The outlook for economic growth has worsened," he said, adding that the turmoil might continue into next year.
Correspondents day the remark could hint at a possible rate cut from the current level of 2%.
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