From Dragon Quest Wiki
The Flying Bed is one of the vehicls in Dragon Quest VI and can be rode in the dream world. You can obtian the flying bed by doing a few quests in Clearvale, which needs the Flying Carpet to access. you can also go to clearvale in the real world, but cannot get the bed, unlike the carpet and the pegaus (Peggy Sue: can get wings later in game.) which can be opened in both the real world and the dream world. The bed is just like the carpet by the fact that it can only travel over grass plains, water and rocks in the water.