So, I did the quests for that wizard Neloth. And he said there was a bed and chest I could use there. But all the ones I find say they're owned. Where is mine??

I think its a bug.
I cant find mine either and Ive heard other forumers say the same.

It turns out the steward's house is now mine. Why I didn't check there before I don't know.

Oh that is interesting, thanks for the info

Ok, I've been in the same predicament.
=x

I tied going into the steward's house (it was still locked), and I do in fact own the bed...

...at least in part, the other guy sleeps in it to. So are we really supposed to share this bed?
=/
I can't even take everything out of the chest, so something's definitely not right.