No, "bed" is neither the direct object nor the indirect object of the verb. It is the object of the preposition and the prepositional phrase is adverbial. It needs to be in the ablative because it refers to a static location where something takes place.
i was reading Ovid the other day and in the translator's notes it was mentioned that in ancient Greece (and probably Rome?) weasels and other small furry mammals occupied the role of cats so this kind of makes sense now!