Kara will do her best to ensure that only naps are taken in whatever becomes his batcave equivalent here. Official sleeping will be done in a comfortable bed, whether she has to put him there herself or not. (You sure you want a Kryptonian for your surrogate Alfred/Robin, Bruce?)
"They really don't." A frown. "They don't know how hard those of us who are different have to work to be something resembling normal. It took me years to get down the human act, to blend in. To be someone that nobody would want to pay much attention to. Guess I kind of ruined that."
Except the 'normal' act helped Kara Danvers exist alongside Supergirl. Without her ability to appear unremarkable, she would've had to abandon her civilian identity and worn the cape twenty-four/seven.