"I think he might be guilty, so please turn him over before I start to bomb the beejeezus out of your country because I think he might be guilty?" No, I don't think that would play any better.

Bush would be neither judge nor jury if bin Laden were to go to a U.S. court. He is of the Executive Branch, which is charged with enforcing the laws. So there is no real harm in his saying: I am confident in his culpability and that is why (a) I want him and (b) I will utilize severe measures to ensure his apprehension.

The people who would impugn the integrity of the U.S. courts in such a situation (should it arise) are not going to persuaded from their views before or after the fact, so it doesn't matter much.