Following the multistage design approach, we propose two asymptotically efficient truthful double auction mechanisms, the BC-LP mechanism and the MBC mechanism, for an exchange market with many buyers and sellers. In this market, each buyer wants to procure a bundle of commodities and each seller supplies one unit of a commodity. Furthermore, various transaction-related costs will be incurred when a buyer trades with a seller. We prove that under both mechanisms, truthful bidding is a dominant strategy for all buyers and sellers when the buyers' bundle information and the transaction cost information are common knowledge. The BC-LP mechanism can be implemented by just solving two linear programs, whereas the MBC mechanism has a higher complexity. The empirical study shows that the MBC mechanism achieves higher efficiency over the BC-LP mechanism and that both outperform the KSM-TR mechanism, the only known truthful mechanism for a more restrictive exchange market.