Since there is no single statement of an official "Bush Doctrine" it is hard to be precise in answering this question. However, the overall thrust of what has come to be known as the Bush Doctrine is much more preventive than it is preemptive.
A preemptive war is one where war is going to happen and the question is simply whether to strike first or wait to be struck. An example of preemptive war would if the US had learned of the Pearl Harbor attack plan on December 1, 1941 and struck first to prevent it. Preemptive war is when you know that your enemy is going to attack and you beat them to the punch.
A preventive war is one where the future war might happen and you are trying to prevent that eventuality from occurring. The Iraq War that is synonymous with the Bush Doctrine was preventive. Even if Iraq had had WMD, there was no evidence that they were going to use the WMD to attack the United States. A war with Iraq was not inevitable. Instead, it was undertaken to prevent a possible conflict in the future.
Since the Bush Doctrine allowed for war to prevent possible dangers that might lead to wars in the future, it was preventive. If it had only said that the US would strike first when war was inevitable it would have been preemptive.