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There is great interest in the development of new polar dielectric ceramics and multiferroic materials with new and improved properties. A family of tetragonal tungsten bronze (TTB) relaxors of composition Ba₆M³⁺Nb₉O₃₀ (M³⁺ = Ga³⁺, Sc³⁺ and In³⁺, and also their solid solutions) were studied in an attempt to understand their dielectric properties to enable design of novel polar TTB materials. A combination of electrical measurements (dielectric and impedance spectroscopy) and powder diffraction (X-ray and neutron) studies as a function of temperature was employed for characterising the dynamic dipole response in these materials. The effect of B-site doping on fundamental dipolar relaxation parameters were investigated by independently fitting the dielectric permittivity to the Vogel-Fulcher (VF) model, and the dielectric loss to Universal Dielectric Response (UDR) and Arrhenius models. These studies showed an increase in the characteristic dipole freezing temperature (T[subscript(f)]) with increase B-cation radius. Crystallographic data indicated a corresponding maximum in tetragonal strain at T[subscript(f)], consistent with the slowing and eventual freezing of dipoles. In addition, the B1 crystallographic site was shown to be most active in terms of the dipolar response. A more in-depth analysis of the relaxor behaviour of these materials revealed that, with the stepwise increase in the ionic radius of the M³⁺ cation on the B-site within the Sc-In solid solution series, the Vogel-Fulcher curves (lnf vs. T[subscript(m)]) are displaced to higher temperatures, while the degree of relaxor behaviour (frequency dependence) increases. Unfortunately, additional features appear in the dielectric spectroscopy data, dramatically affecting the Vogel-Fulcher fitting parameters. A parametric study of the reproducibility of acquisition and analysis of dielectric data was therefore carried out. The applicability of the Vogel-Fulcher expression to fit dielectric permittivity data was investigated, from the simple unrestricted (“free”) fit to a wider range of imposed values for the VF relaxation parameters that fit with high accuracy the experimental data. The reproducibility of the dielectric data and the relaxation parameters obtained by VF fitting were shown to be highly sensitive to the thermal history of samples and also the conditions during dielectric data acquisition (i.e., heating/cooling rate). In contrast, UDR analysis of the dielectric loss data provided far more reproducible results, and to an extent was able to partially deconvolute the additional relaxation processes present in these materials. The exact nature of these additional relaxations is not yet fully understood. It was concluded application of the Vogel-Fulcher model should be undertaken with great care. The UDR model may represent a feasible alternative to the evaluation of fundamental relaxation parameters, and a step forward towards the understanding of the dielectric processes in tetragonal tungsten bronzes.