Agree- flying is gross. However, I personally don't think she showered. I've always been perplexed about the suitcase being found at the bottom of the steps. It seems like it must be important to the pieces of this puzzle but I'm not sure how exactly.
To me it signals something happened rather quickly after she got home. (The only reason I can think the suitcase would still be at the bottom of the stairs is if she, or CW, just hadn't had a chance to bring it up yet. Hence something shortly after she got home).
A lot of people do not wear shoes in the house. Leaving the suitcase at the bottom of the stairs at 2am makes sense. Who wants to lug it upstairs. Plus I am sure she would have dirty clothes in there that needed to go into the wash which I figure would be downstairs.