Bush has consistently opposed any economy-wide programme to curb the carbon dioxide emissions that are believed to spur climate change, arguing that it would hurt the US economy.
Opponents of the bill first delayed it, requiring supporters to get 60 votes, and at the same time attacked it over the sensitive issue of petrol prices.
"At the beginning of the summer driving season [you] offer a bill that would send gas prices up another 53 cents a gallon for goodness sake," Mitch McConnell, the Republican leader and an opponent of the bill, told the bill's supporters.
Senator James Inhofe, a Republican who in the past has denounced global warming as a hoax, called the bill "a massive tax increase on the American people".
But Senator Barbara Boxer, a Democrat and one of three chief sponsors of the bill, disputed both assertions.
She said the bill would provide tens of billions of dollars a year in tax breaks for people facing high energy costs and for other measures which could ease the transition from oil, coal and other fossil fuels.
A summary of the measure by its supporters in the Senate said under the bill US greenhouse gas emissions would drop by about two per cent per year between 2012 and 2050, based on 2005 emission levels.
Carbon dioxide, which contributes to the climate-warming greenhouse effect, is emitted by fossil-fueled vehicles, coal-fired power plants, as well as natural sources such as human breath.
Senators John McCain and Barack Obama, the respective Republican and Democratic presidential nominees, were not present for Friday's vote, but both support limiting human-generated emissions.