The American president said the Taliban leadership was being given one last chance.
Mr Bush said: "Full warning has been given and time is running out."
Bin Laden is the top suspect believed to be behind the terrorist attacks on America, which killed thousands of people.
He has been in hiding in Afghanistan since the crisis.
Mr Bush's speech came as the chance of military retaliation on Afghanistan looked more and more likely.
There has already been some gunfire over Afghanistan's capital, Kabul, and the military there claimed they were trying to shoot down an unidentified aircraft.