Sovereigns of Lost Alara says "you may search your library for an Aura card that could enchant that creature".
Could it find a card with Bestow (that can be cast as an Aura), e.g. Ghostblade Eidolon?
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In your deck, cards with Bestow are just normal Enchantment Creatures because that's what is written on the type line.
The Bestow ability only functions in zones that the card cast be cast from (normally your hand). Bestow does nothing at all to a card in your library.
702.102a Bestow represents a static ability that functions in any zone from which you could play the card it’s on.
Even if the Bestow ability did function, Bestow doesn't change your card into an aura unless it is put onto the stack stack by casting it using the Bestow cost.
702.102b As a spell cast bestowed is put onto the stack, it becomes an Aura enchantment and gains enchant creature. It is a bestowed Aura spell, and the permanent it becomes as it resolves will be a bestowed Aura.