The classical view of the structural changes that occur at the ferroelectric transition in perovskite-structured systems, such as BaTiO3, is that polarization occurs due to the off-center displacement of the B-site cations. Here, we show that in the bismuth sodium titanate (BNT)-based composition 0.2(Ba0.4Sr0.6TiO3)-0.8(Bi0.5Na0.5TiO3), this model does not accurately describe the structural situation. Such BNT-based systems are of interest as lead-free alternatives to currently used materials in a variety of piezo-/ferroelectric applications. A combination of high-resolution powder neutron diffraction, impedance spectroscopy, and ab initio calculations reveals that Ti4+ contributes less than a third in magnitude to the overall polarization and that the displacements of the O2- ions and the A-site cations, particularly Bi3+, are very significant. The detailed examination of the ferroelectric transition in this system offers insights applicable to the understanding of such transitions in other ferroelectric perovskites, particularly those containing lone pair elements.