ABSTRACT Galactic microlensing datasets now comprise in excess of 104 events and, with the advent of next-generation microlensing surveys that may be undertaken with facilities such as the Rubin Observatory (formerly LSST) and Roman Space Telescope (formerly WFIRST), this number will increase significantly. So too will the fraction of events with measurable higher order information, such as finite-source effects and lens–source relative proper motion. Analysing such data requires a more sophisticated Galactic microlens modelling approach. We present a new second-generation Manchester–Besançon Microlensing Simulator (MaBμlS-2), which uses a version of the Besançon population synthesis Galactic model that provides good agreement with stellar kinematics observed by the Hubble Space Telescope (HST) towards the bulge. MaBμlS-2 provides high-fidelity signal-to-noise limited maps of the microlensing optical depth, rate and average time-scale towards a 400 deg2 region of the Galactic bulge in several optical to near-infrared pass-bands. The maps take full account of the unresolved stellar background, as well as limb-darkened source profiles. Comparing MaBμlS-2 with the efficiency-corrected OGLE-IV 8000 event sample shows a much improved agreement over the previous version of MaBμlS and succeeds in matching even small-scale structural features in the OGLE-IV event rate map. However, evidence remains for a small underprediction of the event rate per source and overprediction of the time-scale. MaBμlS-2 is available online (www.mabuls.net, Specht & Kerins) to provide on-the-fly maps for user-supplied cuts in survey magnitude, event time-scale and relative proper motion.