Abstract We present a novel interpretation of the previously puzzling different behaviours of stellar populations of the Milky Way’s bulge. We first show, by means of pure N-body simulations, that initially co-spatial stellar populations with different in-plane random motions separate when a bar forms. The radially cooler populations form a strong bar, and are vertically thin and peanut-shaped, while the hotter populations form a weaker bar and become a vertically thicker box. We demonstrate that it is the radial, not the vertical, velocity dispersion that dominates this evolution. Assuming that early stellar discs heat rapidly as they form, then both the in-plane and vertical random motions correlate with stellar age and chemistry, leading to different density distributions for metal-rich and metal-poor stars. We then use a high-resolution simulation, in which all stars form out of gas, to demonstrate that this is what happens. When we apply these results to the Milky Way we show that a very broad range of observed trends for ages, densities, kinematics and chemistries, that have been presented as evidence for contradictory paths to the formation of the bulge, are in fact consistent with a bulge which formed from a continuum of disc stellar populations which were kinematically separated by the bar. For the first time, we are able to account for the bulge’s main trends via a model in which the bulge formed largely in situ. Since the model is generic, we also predict the general appearance of stellar population maps of external edge-on galaxies.