Abstract: Solid state compounds which exhibit non-centrosymmetric crystal structures are of great interest due to the physical properties they can exhibit. The 'hybrid improper' mechanism – in which two non-polar distortion modes couple to, and stabilize, a further polar distortion mode, yielding an acentric crystal structure – offers opportunities to prepare a range of novel non-centrosymmetric solids, but examples of compounds exhibiting acentric crystal structures stabilized by this mechanism are still relatively rare. Here we describe a series of bismuth-containing layered perovskite oxide phases, RbBiNb2O7, LiBiNb2O7 and NaBiNb2O7, which have structural frameworks compatible with hybrid-improper ferroelectricity, but also contain Bi3+ cations which are often observed to stabilize acentric crystal structures due to their 6s(2) electronic configurations. Neutron powder diffraction analysis reveals that RbBiNb2O7 and LiBiNb2O7 adopt polar crystal structures (space groups I2cm and B2cm respectively), compatible with stabilization by a trilinear coupling of non-polar and polar modes. The Bi3+ cations present are observed to enhance the magnitude of the polar distortions of these phases, but are not the primary driver for the acentric structure, as evidenced by the observation that replacing the Bi3+ cations with Nd3+ cations does not change the structural symmetry of the compounds. In contrast the non-centrosymmetric, but non-polar structure of NaBiNb2O7 (space group P2(1)2(1)2(1)) differs significantly from the centrosymmetric structure of NaNdNb2O7, which is attributed to a second-order Jahn-Teller distortion associated with the presence of the Bi3+ cations.