Context. Solar radio bursts (SRBs), such as Type IIs and IIIs, are emitted by electrons propagating through the corona and interplanetary space. Tracking such bursts is key to understanding the properties of accelerated electrons and radio wave propagation as well as the local plasma environment that they propagate through. Aims. In this work, we present a novel multilateration algorithm called BayEsian LocaLisation Algorithm (BELLA) and validate the algorithm using simulated and observed SRBs. In addition, apparent SRB positions from BELLA are compared with comparable localisation methods and the predictions of solar wind models. Methods. BELLA uses Bayesian inference to create probabilistic distributions of source positions and their uncertainties. This facilitates the estimation of algorithmic, instrumental, and physical uncertainties in a quantitative manner. Results. We validated BELLA using simulations and a Type III SRB observed by STEREO A and STEREO B at ±116° from the Sun-Earth line and by Wind at L1. BELLA tracked the Type III source from ∼10–150 R_⊙ (2–0.15 MHz) along a spiral trajectory. This allowed for an estimate of an apparent solar wind speed of v_sw ∼ 400 km s⁻¹ and a source longitude of ϕ₀ ∼ 30°. We compared these results with well-established methods of positioning: Goniopolarimetric (GP), analytical time-difference-of-arrival (TDOA), and Solar radio burst Electron Motion Tracker (SEMP). We found them to be in agreement with the results obtained by BELLA. Additionally, the results aligned with solar wind properties assimilated by the Heliospheric Upwind Extrapolation with time dependence (HUXt) model. Conclusions. We have validated BELLA and used it to identify apparent source positions as well as velocities and densities of the solar wind. Furthermore, we identified higher than expected electron densities, suggesting that the true emission sources were at lower altitudes than those identified by BELLA, an effect that may be due to appreciable scattering of electromagnetic waves by electrons in interplanetary space.