The chart below shows the US Federal deficit by year since 2002 (Source, the White House):
On first glance it seems that George Bush raised the deficit to over $1.4 trillion dollars in 2009 and Obama shrunk the deficit every through 2013, however less than half the 2009 budge it a George Bush accomplishment.
The U.S fiscal year runs from October-September. The President who is in office at the beginning of the fiscal year gets the credit or blame for that year's budget. Since he was in office in October of 2008, George Bush get's credit for the 2009 budget.
In February of 2009 the Democratic Party controlled Congress rammed through the stimulus bill and President Obama. The entire bill for the stimulus ($830 billion) was spent in the 2009 fiscal year. Thus Bush was assigned the stimulus spending even though it was an Obama bill.
If the deficits were meted out with the stimulus in mind they would look more like this:
George Bush was by no means a deficit hawk, but President Obama took Bush's high-spending ways and ramped them into overdrive. He doubled the already high Bush deficits before he cut them in half.