I don't think it should be called a doctrine. I think what the President did in this case was decide to attack and invade Iraq unilaterally, then later in his presidency attempted to construct a philosophy of executive power that conformed to his earlier decision. The inherent risks and costs of this philosophy revealed themselves as soon as he exercised the so-called doctrine for the very first time. This is especially true since we know now that no threat to US national security existed.
So, as opposed to the Truman Doctrine, Nixon Doctrine or the Monroe Doctrine, the Bush Doctrine was, in my opinion, simply self-serving policy justification, and an attempt to create the appearance of some kind of legacy for his presidency.
I think we are seeing now in the aftermath of the military activity in Iraq and also the ongoing problems in Afghanistan the limitations of the Bush doctrine. Whilst it seems reasonable that a country should be able to attack another country if they do pose an "immediate danger," but as highlighted above, there are massive problems when trying to establish what constitutes an immediate danger and likewise there is a difficulty in terms of securing accurate intelligence that honestly reflects the situation. The threat of Saddam Hussein was completely exaggerated and therefore intervention in Iraq was unnecessary, and this is something that is still trying to be worked through in countries such as Britain, who used the threat argument to justify war.