Many real-world applications operate on dynamic graphs that undergo rapid changes in their topological structure over time. However, it is challenging to design dynamic algorithms that are capable of supporting such graph changes efficiently. To circumvent the challenge, we propose a batch-dynamic framework for answering distance queries, which combines offline labelling and online searching to leverage the advantages from both sides - accelerating query processing through a partial distance labelling that is of limited size but provides a good approximation to bound online searches. We devise batch-dynamic algorithms to dynamize a distance labelling efficiently in order to reflect batch updates on the underlying graph. In addition to providing theoretical analysis for the correctness, labelling minimality, and computational complexity, we have conducted experiments on 14 real-world networks to empirically verify the efficiency and scalability of the proposed algorithms.