Bush was generally seen as a buffonish manchild who had NeoCons and Army Generals mostly in control while they distracted him. Most impersonations or takes on Bush generally followed this rule. This rose considerably when, after months of trying to get the UK public to approve for war, Tony Blair got a civil servant to practically doctor up a dossier claiming that Iraq absolutely had billions of Weapons of Mass Destruction. Oddly everyone glossed over why Blair did it and mostly assumed it was purely for Bush's benefit. But he was part of the Labour party so he got away with it.
Best examples from around the time period.
Of course everyone magically forgets how much everyone hated Bush. But instead is nostalgic for him, but Biden has the potential same issue where media showing him as "out of it" in parody might get him off the hook for whatever policy he cooks up.