This paper presents a novel safety property verification approach for component-based systems modelled in BIP (Behaviour, Interaction and Priority), encompassing multiparty synchronisation with data transfer and priority. Our contributions consist of: (1) an on-the-fly lazy predicate abstraction technique for BIP; (2) a novel explicit state reduction technique, called simultaneous set reduction, that can be combined with lazy predicate abstraction to prune the search space of abstract reachability analysis; (3) a prototype tool implementing all the proposed techniques. We also conduct thorough experimental evaluation, which demonstrates the effectiveness of our proposed approach.