What were the roots of the bush administration’s policy in iraq?

The idea that the best defense against terrorism in the world was to use American power to spread democratic values in countries that were potential breeding grounds for terrorist activity.

This sort of policy agenda was part of the "neoconservative" view of a number of  President George W. Bush's advisers -- especially some who had also served in the administration of his father, President George H.W. Bush.  In the wake of the 9/11 attacks, there was a desire to push American values and not be shy about doing so with the use of American military might.  Sometimes referred to as the "Bush Doctrine," the core ideas were that the United States could pursue this goals on its own (without need for United Nations partnerships), that preemptive strikes were allowable against countries that harbored terrorists, and that regime change for the sake of promoting democracy was a good strategy.  

Things in Iraq haven't worked out as favorably as the Bush administration had hoped.