It wasn't Obama who found it him, derp. It was the CIA using intel they had been gathering for a long time, back to when Bush was still in office, using interrogation techniques that people like Obama cried about before he became President.
One thing I have to give Obama credit for - Once the CIA told him they thought they had a solid lead, he went all in. He did blink or flinch away from kill bin Laden.
Bush would have done the same.