The application of seismology diagnostic techniques to transverse oscillations of coronal waveguides is a source of information on the magnetic field strength. However, a number of assumptions on the density of the structures are needed to infer this physical quantity from the observed oscillation properties. We applied Bayesian inference to the problem of determining the magnetic field strength from the observed period or phase speed of transverse oscillations. This is done by computing the marginal posterior probability density functions for the waveguide density, the density contrast and the magnetic field strength using properties of transverse oscillations under the assumption that they can be modelled as standing or propagating magnetohydrodynamic (MHD) kink modes. The obtained results indicate that the magnetic field strength can be inferred, even if the densities inside and outside the structure are largely unknown. When some information on plasma density is available, the method enables us to self-consistently include this information to further constrain the inferred magnetic field strength.