I found that I can order my companion (Lydia in my case, but guess it doesn't matter) to sleep by pointing at the bed while in "command mode".
What is the point of this? Many of the other commands have some real use, for example asking them to pick things, attack something etc.
I tried to join the companion in bed (yeah I know :)) but once I got out of "command mode" she got out of bed so that failed miserably as well.
Any other ideas? The only thing I can think of right now is maybe let the companion sleep for several hours, then they will get the rest bonus? If so, can this be proven somehow?