Sequential model-based design of experiments (MBDoE) uses information from previous experiments to select run conditions for new experiments. Computation of the objective functions for popular MBDoE can be impossible due to a non-invertible Fisher Information Matrix (FIM). Previously, we evaluated a leave-out (LO) approach that design experiments by removing problematic model parameters from the design process. However, the LO approach can be computationally expensive due to its iterative nature and some model parameters are ignored. In this study, we propose a simple Bayesian approach that makes the FIM invertible by accounting for prior parameter information. We compare the proposed Bayesian approach to the LO approach for designing sequential A-optimal experiments. Results from a pharmaceutical case study show that the Bayesian approach is superior, on average, to the LO approach for design of experiments. However, for subsequent parameter estimation, a subset-selection-based LO approach gives better parameter values than the Bayesian approach.