Almost half of the nearly 21,000 people in 21 countries who responded to the poll published on Wednesday made no distinction between the Bush administration and the US itself.
They saw US influence in the world as largely negative and viewed Americans negatively as well.
In none of the countries polled was there support for contributing troops to Iraq.
"Negative feelings about Bush are high and are generalising to
the American people who re-elected him," said Steven Kull, director of the programme on international policy attitudes at the University of Maryland, which carried out the poll in collaboration with international polling company GlobalScan.
"This is quite a grim picture for the US," he added.
Need for diplomacy
In US Senate confirmation hearings, Bush's nominee as secretary of state, Condoleezza Rice, on Tuesday acknowledged the need for more diplomacy and for the rebuilding of alliances.
She said US interaction with the world "must be a conversation, not a monologue".
Typically, one British contributor to the World Service website on Wednesday said Bush's re-election "means more pollution, war and social injustice [particularly in America]".
"Whatever happened to the freedom-loving, forward-thinking, right-minded people that made America the envy of the rest of us?" he asked.
On average across all countries, the BBC poll indicated that 58% of people think Bush's re-election has made the world more dangerous.
Only in three countries, Poland, India and the Philippines, was there a majority of support for Bush.
Even in traditional US allies such as Germany, France and
Britain, as well as in neighbouring Canada and Mexico, sentiment was predominantly anti-Bush.
In Turkey, a US ally and the only Muslim member of the North Atlantic Treaty Organisation, 82% of those polled said Bush's re-election was bad for world peace.
Anti-Bush sentiment was also strong in Latin America, with 79% of those polled in Argentina and 78% in Brazil describing his re-election in negative terms.
In the poll, which took place from 15 November to 5 January,
500 to 1800 people were surveyed in each country.
The margin of error in extrapolating the results to the entire population was placed between 2.5 and four percentage points, depending on the country.