There are now, in principle, a limitless number of hybrid van der Waals heterostructures that can be built from the rapidly growing number of two-dimensional layers. The key question is how to explore this vast parameter space in a practical way. Computational methods can guide experimental work however, even the most efficient electronic structure methods such as density functional theory, are too time consuming to explore more than a tiny fraction of all possible hybrid 2D materials. Here we demonstrate that a combination of DFT and machine learning techniques provide a practical method for exploring this parameter space much more efficiently than by DFT or experiment. As a proof of concept we applied this methodology to predict the interlayer distance and band gap of bilayer heterostructures. Our methods quickly and accurately predicted these important properties for a large number of hybrid 2D materials. This work paves the way for rapid computational screening of the vast parameter space of van der Waals heterostructures to identify new hybrid materials with useful and interesting properties.