How does Bush think?

I think that is the wrong question. The real question to ask is "How are decisions made in the White House?" Let's look at how they approach the Iraq set of problems.

People need to drop back and step away from trying to figure out what is on Bush's mind. It is my best guess that the White House is a triumvirate, with Rove as domestic czar and leader of the Republican party mechanism, Cheney as the foreign policy/military/Intelligence czar, and Bush as the nice-guy front man who gives the speeches written for him. You may notice a big gap in that. There is no policy expert who knows how things are really done within government (as opposed to merely giving orders, delegating, and firing those who don't toe the line), and there is no economics expert.

What coordination actually occurs is mostly at the second level of staff, but these guys make the final decisions. Staff members don't present problems. They present (acceptable) solutions.

The problem for the triumvirate with Iraq is that Iraq was a Cheney initiative that is now bleeding over to become a Rove problem. It has become a coordination problem within the triumvirate. But Bush is a "delegator", not one who coordinates between different points of view. Cheney is a high-ego person who is not ready to admit a mistake in Iraq, so the domestic problems doubtless already perceived by Rove are not going to influence him. All three operate on the strategy that if you decide something will be done and refuse to admit error or compromise, your opponents/enemies will end up compromising away their power and giving you what you want.

The absence of a central coordinator and of a government policy expert is requiring military people aware of the disaster that is Iraq (Our potential military collapse not the least of the problems) to use public political pressure to try to influence the triumvirate. This runs up against the "never admit error or mistake" attitude all three have. This is a dysfunctional group made up of less than fully functional individuals. You will never be able to understand "Bush's policy." It is a resultant of the individual positions and the relative political power of the individuals involved.

The vaunted Bush loyalty is key in this. Failure by a loyal minion is rewarded by promotion - See Bolton and Wolfowitz. Rove and Cheney are in place, cannot be promoted, and will not be chastised, corrected, abandoned or left to hang out to dry. These two, with Bush, are the current "Presidency." Failure by one is failure by all. For response failure or error, see the "Refusal to admit error" above.
Bush takes his marching orders from the other two members of the triumvirate. Remember when he asked about the third tax cut and Cheney cut him off?

Look to the group processes, not the individaul ideas. America's problem is not "How Bush Thinks." It is "How the dysfunctional group Presidency fails to function." The failures can be grouped into failure to listen to bad news, failure to coordiate between the members of the triumverate, failure to make government function efficiently, and failure to apparently even comprehend economics and the economic impacts of the federal government on American society and on international trade. There is also a total failure to understand how America relates to the rest of the world. As important as this is, it seems to me to be minor compared to the basic dysfunctions of the White House.

This is a set of problems caused by a dysfunctional group trying to run things, not just a question of "How does Bush think." But it is still Bush's individual responsibility.