how big of a hole and how did you burn it. This is probably a fiberglass tub and they make fiberglass repair kits in the home improvement sections and auto body sections of places like walmart and auto repair stores.(look for the Bondo brand) I don't know if it will work with your particular hole.
Call your landlord to let him know. If the bottom of the tub is raised above the floor so the drain piping can be installed under it and above the floor, then those will be hard to find.