Update: Polar3D has changed their pricing structure. They now offer a school license ($500) which allows connecting unlimited printers and also has some edcuation centric offerings included such as direct integration with Google Classroom and Drive as well as direct printing from TinkerCAD.
I've had 3D printers in my classroom for a few years now. I started with Makerbot Replicator 2's and now I have several Flashforge Finders. The newer model Finders (aka Finder 2 and Finder 3) come with the ability to print wirelessly over the network using the FlashPrint application OR by using the PolarCloud via polar3d.com. Polar3D works with many printer models. It can also work with older model printers (like my Makerbot Rep 2's) using the Octoprint plugin. With older printers, you'll need a machine connected to the printer, but then you can print remotely! Even more useful? You can use Polar3D to print DIRECTLY from a Chromebook! Your students can simply "Sign in with Google", to access Polar3D.com.
So, go ahead, sign up or simply login with Google (or many other social providers). Connect your printer and start printing remotely!