We report a series of layered superconductors, anti-ThCr2Si2-type RE2O2Bi (RE = rare earth), composed of electrically conductive Bi square nets and magnetic insulating RE2O2 layers. Superconductivity was induced by separating the Bi square nets as a result of excess oxygen incorporation, irrespective of the presence of magnetic ordering in RE2O2 layers. Intriguingly, the transition temperature of all RE2O2Bi including nonmagnetic Y2O2Bi was approximately scaled by unit cell tetragonality (c/a), implying a key role in the relative separation of the Bi square nets to induce superconductivity.