Hey, did you ever get your dog bed felted?
I made a suggestion of how you might do this on another thread, but you may not have seen it. I suggested using a regular size washer at a laundromat because I think the dog bed will fit in it just fine. And I think you can open the lids of those machines (maybe?).
The other suggestion I had was to put it in a dirty laundry bag like college kids often use to bring their dirty clothes home to wash.
Let us know how it turned out!!