One of the goals of the InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission is to constrain the interior structure of Mars. We present a hierarchical transdimensional Bayesian approach to extract phase velocity dispersion and interior shear-wave velocity (VS) models from a single seismogram. This method was adapted to Mars from a technique recently developed for Earth (Xu & Beghein, 2019). Monte Carlo Markov Chains (MCMC) seek an ensemble of one dimensional (1-D) VS models between a source and a receiver that can explain the observed waveform. The models obtained are used to calculate the phase velocities of fundamental and higher modes at selected periods, and a subsequent analysis is performed to assess which modes were reliably measured. An advantage of our approach is that it can also fit unknown data noise, which reduces the risk of overfitting the data. In addition, uncertainties in the source parameters can be propagated, yielding more accurate model parameter uncertainties. In this paper, we first present our technique and discuss the challenges stemming from using a single station to characterize both structure and the source and from the absence of a Mars reference model. We then demonstrate the method feasibility using the MSS blind test data and our own synthetic data, which included realistic noise levels based on the noise recorded by InSight.