For speakers of non-American english I should probably explain that the designation of George W. Bush as a bully is not complimentary. Morever, considering that Teddy Roosevelt's use of the "bully pulpit" has historically been viewed as positive, the identification of bullying behavior as a destructive force is fairly recent and perhaps not very well understood.
In any event, since I have concluded for myself that George W. Bush is a bully, I think it only fair to explain the basis of that judgement. And to do that, I think we have to start with how and why humans interact.
It probably seems logical to most people to assume that other people's behavior towards them is a response to how they act themselves. This assumption, after all, is the basis of the so-called "golden rule" which enjoins us to "do unto others as you would have them do unto you."
This assumption also tends to support the individual inclination to be in control of one's own behavior, determinative of what happens in the future, as well as the behavior of others. In other words, we assume the world to be as we would like it to be.
The facts, however, demonstrate that the world is quite different. Indeed, the world is full of people (often referred to as "innocent victims" or "collateral damage") whose injuries are totally unconnected to anything they have or have not done. Which is not to say that the injuries are either accidental or unintended. The perpetrators of these acts mean to cause harm. But not to affect the behavior of the victims. Indeed, the behavior of the victims is irrelevant to their interests. Their purpose is to attack someone who can't or won't fight back in order to affect the behavior of someone who might.
That's why this kind of aggression needs to be so overt and public (on the playground, the world's tallest buildings, in front of "embedded" reporters). The behavior of the audience, not the immediate target, is the issue. Or rather, it's the non-behavior of the audience. The bully attacks those who are weaker (or unsuspecting) and hopes to prevent those who are stronger from confronting him directly.
In other words, the bully is a coward. He doesn't rely on third parties to fight his battles; he inflicts injury on third parties in order to protect himself--to "feel" safe. But is he? And how long will that feeling last? More to the point: How long does intimidation last?