Other mistake: When Mr Bean has messed the painting up, he takes it to a room to get the pen ink off, this room is labeled "employees washroom" and inside its a workshop. (00:42:25)
Other mistake: When Bean was shaking the unconscious daughter in the hospital bed trying to revive her, the daughter licks her lips to moisten them right before Bean climbs on the bed. (01:15:50)
Answer: In the context of the movie, the "damage" has already been done, so-to-speak... he's already in the shower with Bean. And since he's also in a big rush to get to the museum, he decides to just keep showering. (In a meta, behind-the-scenes sense, it's also just funnier for him to stay in the shower rather than get out and wait for Bean.)
TedStixon