Although President Bush was a conservative in many ways, this law is (in most of its aspects) the product of a more liberal approach. The law fits better with liberal ideas because it uses the power of the federal government to try to impose a certain vision of progress on the schools of the country.
Conservatives tend to distrust large, top-down solutions for social problems. They are not inclined to trust the federal government to be able to come up with the best solutions for such problems. Liberals tend to put much more trust in the federal government and are typically much more content to see it set standards (as it did in NCLB) rather than letting states be in charge.
As a side note, we can see that conservatives are generally opposed to this sort of law in the comments of Rick Santorum. Santorum, running for president, has said that the federal government (and even state governments) should not be involved in education.