We present a new approach for learning the structure of a treewidth-bounded Bayesian Network (BN). The key to our approach is applying an exact method (based on MaxSAT) locally, to improve the score of a heuristically computed BN. This approach allows us to scale the power of exact methods---so far only applicable to BNs with several dozens of nodes---to large BNs with several thousands of nodes. Our experiments show that our approach outperforms a state-of-the-art heuristic method.