Excellent advice, Ginger! I can't think of a thing to add to what you said. Thanks!
Ghilly
Is she ok now? Or still sick?
A pup who throws up more than once or twice needs to go to the vet because there is the danger of dehydration. Puppies are more susceptible.
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. At least it didn't get any further down her digestive tract to cause a blockage)
However if it were more like small dots of black, that could mean there was some bleeding in her stomach.
Best to take her to be checked over.