For spring/summer, you'll need either a separate bugnet to go over your hammock or a hammock with an integrated bugnet. As mentioned, you'll need the other components to hammock camp. You may already have a tarp, a sleeping pad can serve as under insulation, and a sleeping bag can be used for top insulation. If you don't have any of these, you'll definitely need to acquire them to be comfortable out there.
Don't let life get in the way of living.