If there have been crimes committed by Bush (and I firmly believe there have been SERIOUS ones), they should investigate the s*** out of him and all of the administration officials. I think Obama will be preoccupied with other things for a while. One can only hope that Bush and Cheney are not give time to destroy documents.
If I were Obama I would set the Justice Department to work on my first day to make sure that no evidence is "lost" or is "accidentally" destroyed, which I would I would assume is likely to happen, if it hasn't already.
"Responsibility" is not in the Bush/Cheney vocabulary, unless it's someone else committing a crime. Look at Bush's record as Governor of Texas and all the execution warrants he signed. Bush should be held to the same values he espoused as Governor and President.
To answer your question, Bush demanded accountability from anyone outside his Administration, it would be hypocritical and immoral for him to block any attempt to hold him accountable for his decisions or actions. The President cannot hide behind privilege if there have been war crimes or negligence while he was steering the ship.
There should be a full investigation into Administration activities for the full eight years. If there is evidence that there were illegalities committed, the guilty parties should be handed over to the proper authorities. This includes the World Court or the War Crimes Tribunal.
Sorry for the long - windedness.