Ion rejection properties of cylindrical nanopores with bipolar fixed charge distributions have been investigated theoretically by means of an approximate model based on the Poisson-Nernst-Planck (PNP) theory and accounting for the electroosmosis phenomenon The approximate model has been shown to give results that are in good agreement with the full 2D PNP approach for the narrow and weakly charged pores considered in this work Pressure-induced rectification of salt flux has been put in evidence as a result of the broken symmetry of the fixed charge distribution on the pore walls. The model also elucidates that pressure-induced transport is controlled by different pore regions depending on the magnitude of the pressure difference across the nanopore The existence of an optimal pressure difference (i.e., leading to the highest salt rejection) has been put in evidence when there is a region within the nanopore that is more repulsive than the pore entrance with respect to a given electrolyte. For moderate pressure differences, our results show that nanopores with bipolar charge distributions can lead to close rejections for both 2-1 and 1-2 asymmetric electrolytes. This is a specific property of bipolar nanopores because these performances cannot be obtained with homogeneously charged nanopores, which strongly reject electrolytes with divalent co-ions but are much more permeable to electrolytes with divalent counterions. This work benefits the design of nanoporous systems with targeted distribution of ionizable surface groups for advanced membrane separations.