Does bestow work differently from casting an aura normally in terms of targeting?

When you cast an Aura normally, it uses the rules for Auras on the stack: it targets whatever its enchant ability specifies (e.g., "enchant creature" means it targets a creature). If that target becomes illegal before the Aura resolves, the spell is countered by the rules and goes to the graveyard (CR 303.4f, 608.2b).

Bestow works differently in a crucial way. A bestow spell is not an Aura while it is on the stack — it is a creature spell that also happens to target a creature (CR 702.102a). Because it is a creature spell, if its target becomes illegal when it tries to resolve, the targeting rules counter it... but CR 702.102d specifies that if a bestow spell's target is illegal on resolution, it simply stops being an Aura and resolves as a creature permanent instead of going to the graveyard.

Another difference: because bestow makes the spell a creature spell (not an Aura spell) on the stack, it cannot be "Aura-proofed" by effects that specifically interact with Aura spells being cast. Conversely, spells that counter creature spells can counter a bestow spell.

Example: You cast Eidolon of Blossoms with bestow, targeting your opponent's Grizzly Bears. Your opponent responds by destroying Grizzly Bears. When Eidolon tries to resolve, its target is gone — but instead of fizzling, Eidolon resolves and enters the battlefield as a 2/2 enchantment creature on your side.

In summary: normal Auras go to the graveyard if their target vanishes; bestow spells instead fall back to becoming creatures (CR 702.102d). Also, the spell type on the stack is creature, not Aura, which affects what spells and abilities can interact with it.