Say you exile a creature such as Eidolon of Countless Battles with a Nightveil Specter or Ashiok, Nightmare Weaver. Can you cast it with bestow as an enchantment aura or can you only cast it as a creature?
When a card is exiled with Nightveil Specter, you may play it in any way it could normally be played under all the normal restrictions (such as timing, paying costs, etc). In the case of exiling Eidolon of Countless Battles (or any other bestow creature), this means you can pay the bestow cost to cast the spell as an enchantment aura.
When a creature card is exiled with Ashiok, you can later use his -X ability to place it on the battlefield. Notice the difference here: You do not cast it. Since it is not cast, you do not have the option of paying the alternate bestow casting cost and casting it as a enchantment aura. Thus, you cannot bestow a creature card exiled with Ashiok.