Monobismuthides of lutetium and yttrium are shown as representatives of materials which exhibit extreme magnetoresistance and magnetic-field-induced resistivity plateaus. At low temperatures and in magnetic fields of 9 T, the magnetoresistance attains orders of magnitude of 104% and 103%, on YBi and LuBi, respectively. Our thorough examination of electron-transport properties of both compounds shows that observed features are the consequence of nearly perfect carrier compensation rather than of possible nontrivial topology of electronic states. The field-induced plateau of electrical resistivity can be explained with Kohler scaling. An anisotropic multiband model of electronic transport describes very well the magnetic field dependence of electrical resistivity and Hall resistivity. Data obtained from the Shubnikov–de Haas oscillation analysis also confirm that the Fermi surface of each compound contains almost equal amounts of holes and electrons. First-principle calculations of electronic band structure are in a very good agreement with the experimental data.