Does bestow cause the aura to return to the battlefield as a creature if the enchanted permanent dies?

Bestow is a keyword ability that lets you cast a card either as a creature or as an Aura enchantment. When you cast it using its bestow cost, it enters the battlefield as an Aura enchanting a permanent. However, it retains a special rule: if it ever stops being an Aura while on the battlefield, it immediately becomes a creature instead of going to the graveyard. This is covered by CR 702.102d (Bestow).

The key moment is when the enchanted permanent leaves the battlefield. Normally, an Aura whose enchanted permanent has left would be placed in the graveyard as a state-based action (CR 704.5m). But Bestow overrides this: rather than being put in the graveyard, the bestow card stops being an Aura and becomes a creature permanent on the battlefield. It stays in the same zone (the battlefield) and simply changes its characteristics.

This transition happens as a state-based action check. The Aura losing its enchanted object causes it to cease being an Aura, and because Bestow grants it the ability to exist as a creature, it stays on the battlefield as one. It does not enter the battlefield again — it was already there — so no 'enters the battlefield' triggers fire.

Example: You have a Leafcrown Dryad (bestow) enchanting your Elvish Mystic. Your opponent destroys Elvish Mystic with Lightning Bolt. Instead of Leafcrown Dryad going to the graveyard, it remains on the battlefield as a 2/2 creature with Reach. No 'enters the battlefield' trigger occurs because it never left the battlefield.

Note: if the bestow permanent is somehow removed from the battlefield by another effect while it is still an Aura (e.g., exiled), it goes to the exile zone as a card, not as a creature — this rule only applies when it loses its enchanted permanent while already on the battlefield.