Perovskite oxides with Bi(3+) on the A site are of interest as candidate replacements for lead-based piezoelectric ceramics. Current understanding of the chemical factors permitting the synthesis of ambient-pressure-stable perovskite oxides with Bi(3+) on the A site is limited to information derived from average structures. The local structure of the lead-free ferroelectric perovskite Bi(Ti(3/8)Fe(2/8)Mg(3/8))O(3) is studied by reverse Monte Carlo (RMC) modeling of neutron scattering data. The resultant model is consistent with the structure derived from diffraction but reveals key extra structural features due to correlated local displacements that are inaccessible from the average unit cell. The resulting structural picture emphasizes the need to combine symmetry-averaged long-range and local analysis of the structures of compositionally complex, substitutionally disordered functional materials. Local correlation of the off-axis displacements of the A site cation produces monoclinic domains consistent with the existence of displacement directions other than R (<111>(p)) or T (<100>(p)). The Bi displacements are correlated ferroelectrically both in the polar direction and orthogonal to it, providing evidence of the presence of monoclinic domains. The octahedral cation environments reveal distinct differences in the coordination geometry of the different B site metal ions. The local nature of these deviations and correlations makes them inaccessible to long-range averaged techniques. The resulting local structure information provides a new understanding of the stability of pure Bi(3+) A site perovskite oxides.