We propose an efficient procedure for estimating free energies along an external parameter in adaptive Monte Carlo methods. Using Bayes formula, the conditional expectation used to adapt the biasing force given the external parameter is replaced by an average involving the conditional probability of the external parameter given the sampled configurations. We apply the procedure to a structural transition in a cluster and to the migration of a crystalline defect along a reaction coordinate. We observe that the proposed average speeds up the convergence of the adaptive biasing force towards the mean force along the external parameter, compared to simulations using the standard conditional expectation. The proposed procedure is also able to iteratively construct a biasing potential fully compensating the free energy along the reaction coordinate with two practical advantages over standard adaptive procedures: (i) the second derivatives of the reaction coordinate are not needed, (ii) no biasing potential is differentiated to generate the dynamics.