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A first-principles study of the tetragonal tungsten bronze (TTB) K4Bi2Nb10O30 has suggested that the Bi 6s lone pair causes in-plane polarization (within the a–b plane), corresponding to the one found in Pb5Nb10O30 (PN), in contrast to the out-of-plane polarization (along c) found in most TTBs. Replacing PN with KBN potentially opens for a lead-free analogue to morphotropic phase boundaries known in TTBs based on PN. Here, we report on the synthesis and properties of A4Bi2Nb10O30 (ABN, A = Na, K, Rb) with the objective to determine the structure and electrical properties, paying particular attention to the role of the Bi 6s lone pair. The ABN materials were synthesized via conventional solid-state synthesis in a two-step process. Convergent-beam electron diffraction demonstrated a centrosymmetric tetragonal space group for the two compounds KBN and RBN, and ferroelectric polarization–electric field measurements confirmed the lack of hysteretic behavior in line with the observed centrosymmetric symmetry. Non-ambient powder X-ray diffraction demonstrated the signature of a phase transition for KBN and RBN, as several weak satellite reflections vanished during heating and reappeared upon cooling. Dielectric spectroscopy supported the observation of an anomaly due to the presence of a weak maximum in the electrical permittivity at temperatures corresponding to the disappearance of the satellite reflections. Possible explanations for the absence of polarization in ABN TTBs are discussed with particular attention to the suppression of the 6s2 lone pair effect of Bi and the size of A-site cations in the TTB crystal structure.