This paper presents Bayesian inference procedures for the continuous time mover-stayer model applied to labour market transition data collected in discrete time. These methods allow us to derive the probability of embeddability of the discrete-time modelling with the continuous-time one. A special emphasis is put on two alternative procedures, namely the importance sampling algorithm and a new Gibbs sampling algorithm. Transition intensities, proportions of stayers and functions of these parameters are then estimated with the Gibbs sampling algorithm for individual transition data coming from the French Labour Force Surveys collected over the period 1986-2000.