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Relay selection (RS) has widely been studied in the literature, and an opportunistic source selection (OSS) protocol with a single relay has recently been proposed. Since RS and OSS could individually improve the performance of cooperative diversity networks, optimum combining of RS and OSS is an interesting topic. In this paper, we optimally combine RS and OSS in the sense that the mutual information is maximized, and we propose a joint RS-OSS protocol in an amplify-and-forward (AF)-based bidirectional cooperative diversity network, which consists of two different end-sources and multiple relays. In this network, a best source is selected to transmit data to the other source with the help of a selected best relay in an opportunistic manner, depending on channel conditions. Then, to show the performance of the joint RS-OSS, we derive the outage probability and the average bit error rate (BER) for M-quadrature amplitude modulation (QAM). Numerical results confirm that the derived outage probability and the average BER expressions are very accurate. In addition, we find that the proposed joint RS-OSS considerably outperforms both RS and OSS in terms of outage probability and average BER and that the performance is highly dependent on relay location. The obtained outage probability and average BER will help the design of reliable bidirectional cooperative diversity networks in determining the system parameters, such as relay location, and the transmission power at source and relay.