Context. Different modes of oscillations are frequently observed in solar prominences, and prominence seismology helps estimate important physical parameters such as the magnetic field strength. Although the simultaneous detection of longitudinal and transverse oscillations in the same filament is not common, such rare observations provide a unique opportunity to constrain the physical parameters of interest. Aims. In this study, we aim to estimate the physical parameters of prominences undergoing simultaneous longitudinal and transverse oscillations. Methods. We applied Bayesian seismology techniques to observations of longitudinal and transverse filament oscillations to infer the magnetic field strength, the length, and the number of twists in the flux tube holding the prominence plasma. We first used the observations of longitudinal oscillations and the pendulum model to infer the posterior probability density for the magnetic field strength. The obtained marginal posterior of the magnetic field, combined with the observations of the transverse oscillations, was then used to estimate the probable values of the length of the magnetic flux tube that supports the filament material using Bayesian inference. This estimated length was used to compute the number of twists in the flux tube. Results. For the prominences under study, we find that the length of the flux tubes supporting the quiescent prominences can be very large (from 100 to 1000 Mm), and the number of twists in the flux tube is not more than three. Conclusions. Our results demonstrate that Bayesian analysis offers valuable methods for parameter inference in prominence seismology.