I would be inclined to take her to the vet anyway, because throwing up
bile is not a sign that the puppy
is hungry, it's a sign that something is amiss. It could be anything. An upset stomach, an infection, a foreign body...etc Did you, or the people you got your puppy from make sure she had her vaccinations?
I wonder what the black thing was? Was it an object of any kind? If she had swallowed some object, she would be likely to vomit it back (which is the best-case scenario.