On the other side of the fence, I never take off my packer, not even to clean it (I clean it while keeping it attached). Although I like taking my binder off to shower -- my chest is small, and binding has made them look like I'm just a fat guy, so it actually helps some, haa.
But when I was little and would take baths with my mom, she'd cover herself with a rag. I copied that for a while. That generally only helps with bathing, if you'd like a seated shower.