If I cast a card with Bestow, using it's Bestow cost, it will be attached to a creature as an Aura. Is it still a Creature? Can it be targeted with something that targets only creatures? And does it count as a creature for something like Beast of Burden?

I assume not, as there are multiple references that say “it becomes a creature again”, but it's not spelled out explicitly like it is that it is both an Enchantment and a Creature when it's not attached.

Is this just implied by “it becomes an Aura enchantment and gains enchant creature”?

No to everything.

When an effect changes an object's type without mentioning that it keeps previous types, it does lose previous types. As long as it's attached to a creature, it is a non-creature enchantment. When the effect ends, the object will have its printed types, namely creature and enchantment.

Daniel Kitachewsky
L3, Paris, France
Rules NetRep