The formation of molecular aggregates and assemblies is an important process across chemistry, biology, and materials science. In applications such as crystal structure prediction, a balance between high accuracy and computational speed is highly desirable. We present a new method for predicting approximate bimolecular potential curves using dispersion-corrected Harris approximate-density functional theory and an improved estimate of the bimolecular electron density. Our results on benzene dimer and thiophene dimer yield potential energy curves within a few percent of MP2 theory and a speedup of ~10x over conventional density functional methods. The code is highly parallel and gives greater speedups on larger systems and basis sets.