Not as tough as most seem to think. Seeing as he had the most eventfull(IMO, and most would probably agree) Presidency since FDR. Most of the events he had nothing to do with in terms of cause, but as a Conservative Republican I can say he failed at almost all of them. But with the Dotcom/911 Recession, 911 itself, Afghanistan, Iraq, Katrina, the Global Financial Crisis, ect, he had many chances to turn himself into something great.
Here is, IMO, a basic(but opinionated seeing as this is as much a political question as it is a history question) idea of how he could have handled most of the problems that have occured under him.
Dotcom Recession: Honestly, this one ended relatively fast. His response was not bad. Remember, most Neocons were saying in 05 and 06 that even if Bush had screwed up in the Middle East that the economy was going well. Though, this recession would likely be worse if the current economic crisis is to be avoided. If the Dotcom recession ends quickly he can take credit for the recovery while being able to claim he inherited it(similar to Obama's current situation on a much smaller scale).
911/Afghanistan: Handle 911 in a similar way(he was extremely popular after it, so he can still score political points off of it as OTL). Go in to Afghanistan with more force and capture Bin Laden one way or another. Work with Iran(he can start to build a reputation as someone willing to listen to the "other side") and if at all possible gain more cooperation from Pakistan. Turn Afghanistan into a relatively functioning Middle Eastern Democracy.
Iraq: Avoid it. Have information come out saying Iraq has no WMDs.
Katrina: Have someone, Federal, State, or Local, build decent levees. Have 3 levels of government simply work better(It doesn't take much to have that happen). Maybe without so many resources overseas(no Iraq) Bush could send in more national guard units. Maybe he could do something that appears brave, like going in to the city himself(in the safest place in the city of course) during the storm.
Current Economic Crisis: Don't have the Federal Reserve Artificially Lower Interest Rates during the recession earlier in the decade. You can blame deregulation, bad regulations, ect, all you want, but IMO the Fed caused it. If the Fed doesn't lower interest rates so greatly then the Dotcom recession will be worse, but still not severe, and the current crisis is going to be butterflied away.
Fiscal Responsibility: No Iraq is a good place to start. But he still needs to cut spending(IMO). Getting SS reform through Congress is a good place to go besides that. No Medicare Part D is also a potential cut(or rather something not created) that could occur.
Israeli-Palestinian Conflict: Maybe, just maybe, he could use the US's influence to bring a long term solution to the conflict. He could perhaps find some sort of compromise. If he works with Iran(and some other "enemy" states) then he could perhaps be trusted much more around the globe.
If all of this happens, and I don't think any single thing listed is ASB, then maybe he could be seen as one of the best ever.
Wrong, your mentioning of Afghanistan becoming a democracy is totally ASB. You can't have Afghanistan and Democracy in the same sentence.