If showers are not a part of your routine, then, when showering, your mind will be preoccupied with things like "how to shower," "how not to slip," "how not to get burned with hot water," "how to control water temperature," etc., and will not be able to achieve the state of relaxation necessary for generation of new ideas.

The key is that the activity has to be both relaxing and routine (double "r"...). For you, it's bathing, for others it's showering, yet for others it's walking in the woods. If the activity is not relaxing, you will be preoccupied with how to control it and with resulting stress. If the activity is not routine, you will be focused on its novelty rather than letting your mind wander on its own.