Well, let's take a look at how that works.
The responsibility for causing a problem is not the same thing as the responsibility for solving a problem. Calvin Coolidge was POTUS for most of the 1920s. He overspent, he let the balance of wealth get tipped, he oversaw the accumulation of unsupported paper wealth, and a lot of other familiar things. The Wall Street crash that launched the Depression happened less than a year after he left office. Thus, Coolidge is blamed for eight years of policies that led to the Crash.
His successor, Herbert Hoover, completely underestimated the scope of the problem left to him. He called on volunteers to help with economic problems. He let banks and other businesses go out of business, contributing to public fear and instability. He did not put more money into circulation after the crash sucked out a substantial portion of the money supply (though in fairness, the gold standard and Coolidge's overspending limited how much he could have added). Over three years, his policies turned a recession into a Great Depression, and he gets the historical blame for the Depression.
Franklin Roosevelt spent a lot longer dealing with the Depression than did Hoover: almost a decade of high unemployment, anemic economic conditions, and false recoveries. And yet, at no time did it ever change from Hoover's Depression to Roosevelt's Depression.
That's because the responsibility for causing a problem is not the same thing as the responsibility for solving a problem. Causation is fixed in the past, and the past does not change. Coolidge gets blame for the 1929 Crash even though Hoover was President at the time of the actual crash. Hoover made the economy worse, and he gets the blame for that. Roosevelt spent much longer bringing the economy back, but overall his policies caused steady economic improvement, so he gets credit for that.
Though the economic trends that led to the recent crash had built for decades, George Bush was President for the last eight critical years when the worst damage could have been prevented. Even preventing wealth siphoning starting in 2006 and limiting subprime real estate loans starting in 2007 could have turned a crash into a simple real estate slump. He absolutely deserves the blame for the worst economic downturn since the Great Depression, and time won't change that.
However, just to make the contrast clear, President Obama's policies have helped the economy. After the 1929 Wall Street crash, the economy went on a four-year slide. President Obama came into office less than a year after the 2008 crash. Within months, his policies were producing measurable improvements. Had the timing been different, it could have been much worse for us.
Yes, it is still Bush's fault, it will ALWAYS be Bush's fault, and don't let anyone tell you otherwise.