Defects play a key role in determining the properties and technological applications of nanoscale materials and, because they tend to be highly localized, characterizing them at the single-defect level is of particular importance. Scanning tunnelling microscopy has long been used to image the electronic structure of individual point defects in conductors, semiconductors and ultrathin films, but such single-defect electronic characterization remains an elusive goal for intrinsic bulk insulators. Here, we show that individual native defects in an intrinsic bulk hexagonal boron nitride insulator can be characterized and manipulated using a scanning tunnelling microscope. This would typically be impossible due to the lack of a conducting drain path for electrical current. We overcome this problem by using a graphene/boron nitride heterostructure, which exploits the atomically thin nature of graphene to allow the visualization of defect phenomena in the underlying bulk boron nitride. We observe three different defect structures that we attribute to defects within the bulk insulating boron nitride. Using scanning tunnelling spectroscopy we obtain charge and energy-level information for these boron nitride defect structures. We also show that it is possible to manipulate the defects through voltage pulses applied to the scanning tunnelling microscope tip.