Does my Dryad Arbor stop being a creature with a Blood Moon in play?
It does not.

Taken from the rulings found here:

http://gatherer.wizards.com/Pages/Card/Details.aspx?multiverseid=282542

"If Dryad Arbor is changed into another basic land type (such as by Sea’s Claim), it continues to be a creature and a Dryad."

Blood Moon would turn it into another basic land type, in this case a Mountain, so it would continue to be a creature and a Dryad.

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Edit:

With regards to Blood Sun, this too will not stop Dryad Arbor being a creature.

Blood sun simply removes any abilities that are not mana abilities (i.e. abilities that generate mana). Being a creature is not considered an ability, but a type, so Dryad Arbor would still be considered a creature. See below:

305.7. If an effect sets a land’s subtype to one or more of the basic land types, the land no longer has its old land type. It loses all abilities generated from its rules text, its old land types, and any copy effects affecting that land, and it gains the appropriate mana ability for each new basic land type. Note that this doesn’t remove any abilities that were granted to the land by other effects. Setting a land’s subtype doesn’t add or remove any card types (such as creature) or supertypes (such as basic, legendary, and snow) the land may have. If a land gains one or more land types in addition to its own, it keeps its land types and rules text, and it gains the new land types and mana abilities.