We perform direct numerical simulations of a bidisperse suspension of heavy spherical particles in forced, homogeneous, and isotropic three-dimensional turbulence. We compute the joint distribution of relative particle distances and longitudinal relative velocities between particles of different inertia. For a pair of particles with small difference in their inertias we compare our results with recent theoretical predictions [Meibohm et al., Phys. Rev. E 96, 061102 (2017)2470-004510.1103/PhysRevE.96.061102] for the shape of this distribution. We also compute the moments of relative velocities as a function of particle separation and compare with the theoretical predictions. We observe good agreement. For a pair of particles that are very different from each other - one is heavy and the other one has negligible inertia - we give a theory to calculate their root-mean-square relative velocity. This theory also agrees well with the results of our simulations. © 2018 American Physical Society.