I`ve been using the chest in the Tel Mithryn Kitchen for storage .
Even though it marks some items in red(denoting value) , they are never marked as stolen when you retrieve them unless they were stolen to begin with. Survived a 30 day wait with no changes.
As for the bed , it seems you have to share as no extra or exclusive bedding is created once you are part of the "family".
Neloth is a real cheapskate lol
Also , the body of Neloth`s first steward is permanent and doesn`t reset inventory.
You can move her to a convenient location near the front of Tel Mithryn for easy access to your stored items without having to go inside and enduring two loading screens.