We investigate the superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model through quantum Monte Carlo simulations. The Bose-Hubbard model is studied in the presence of site disorder, and the quantum critical point between the Bose glass and superfluid is determined in the grand canonical ensemble at mu/U = 0 (close to rho = 0.5), mu/U = 0.375 (close to rho = 1), and mu/U = 1 as well as in the canonical ensemble at rho = 0.5 and 1. Particular attention is paid to disorder averaging, and it is shown that a large number of disorder realizations are needed in order to obtain reliable results. Typically, more than 100 000 disorder realizations were used. In the grand canonical ensemble, we find Zt(c)/U = 0.112(1) with mu/U = 0.375, significantly different from previous studies. When compared to the critical point in the absence of disorder (Zt(c)/U = 0.2385), this result confirms previous findings showing that disorder enlarges the superfluid region. At the critical point, we then study the dynamic conductivity.