A new sparse estimation method was recently introduced in a pre-vious work to correct biases due to multipath (MP) in GNSS me-asurements. The proposed strategy was based on the resolution ofa LASSO problem constructed from the navigation equations usingthe reweighted-`1method. This strategy requires to adjust the re-gularization parameters balancing the data fidelity term and the in-volved regularizations. This paper introduces a new Bayesian es-timation method allowing the MP biases and the unknown modelparameters and hyperparameters to be estimated directly from theGNSS measurements. The proposed method is based on Bernoulli-Laplacian priors, promoting sparsity of MP biases.