I've offered a plausible opinion about why Bush's polls fell. But the point wasn't to establish that reason -- maybe the fact he led our nation into a catastrophic war and the worst financial meltdown since the Great Depression had no impact on his popularity. It's conceivable. The point, though, was to establish that the reason he wound up hated by the large majority of Americans wasn't because he was a Republican. He was a Republican in early 2000, with opinion polls as high as 63%, and he was a Republican after 9/11 with the highest approval ratings in history. People demonstrated their ability to take the fact he was a Republican in their stride and yet still approve of him. So, to explain how he eventually wound up with approval as low as 25%, at a time when even only 57% of REPUBLICANS liked him, and practically nobody else did, it takes more than just the fact that he was a Republican.
If it had been Clinton, it would have been reported far more negatively, since he wouldn't have had the liberals in the press running interference for him. As happened with LBJ, when Vietnam got ugly, the liberals in the media would have turned on Clinton, along with the centrists and conservatives, and, like LBJ, he'd have been forced to give up the hope of even running for a second term. But since it was a Republican president, he could at least count on continued devotion from the Rupert Murdoch empire and the evangelical pulpits, letting him cling to enough support for a second term in the face of disastrous failure.
Clinton's approval ratings weren't bullet proof. Early on, when the people were mostly judging him by the tirelessly negative reporting in the mainstream press, rather than by Clinton's actual results (which still weren't clear), he was very unpopular. Clinton's approval plunged as low as 37% in his first few months in office. Especially after their cronies in the Travel Office were fired for corruption, the mainstream press absolutely hated Clinton, and took every opportunity to belittle him:
Hell, Time hated Clinton so much they were still at it after he left office:
By comparison, at the same point in the Bush administration, the mainstream press was taking time to document the alleged misbehavior of outgoing Clinton staffers:
http://www.nytimes.com/2001/06/04/us/bush-spokesman-catalogs-pranks-attributed-to-clinton-aides.html
But as much as the corporate press hated Clinton, they couldn't erase his results. Although they could hammer him down to Trump-like approval ratings in his first few months, gradually those ratings rose and rose, until he was the most popular outgoing president in the history of approval polling. Bush followed the opposite trajectory, as befits a miserable failure (amusingly, Bush's name came up first for so long when you Googled "miserable failure" that Google had to manually alter their algorithm to push him down the results list).
The press can have an impact on how a president is perceived, especially in his first year. It can savage him constantly, as with Clinton, driving his ratings into the 30s. Or it can build him up by essentially declaring criticism off limits, as it did with Bush after 9/11, pushing him up into the 90s. But eventually the people start to tune out the press and look at the actual results. At that point, the good presidents tend to rise and the bad ones tend to fall.