We present results of path-integral Monte Carlo simulations of bosons on a two-dimensional square lattice in a random potential of average strength V and with on-site repulsion U. We find that the superfluid density rhos is enhanced by increasing V and U in certain regions of parameter space. By combining the results of rhos, with the behavior of the density-density correlation function on lattices of size up to 10×10, we study the superfluid-to-Mott-insulator transition and the transition from a superfluid to a disorder-localized (``Bose glass'') phase.