We propose a joint power allocation and relay selection scheme for bidirectional relay-enhanced transmission utilizing network coding. The power allocation scheme aims at minimizing the required transmit power while providing the desired quality of service expressed in terms of outage probability. The relay selection task is formulated as a weighted matching problem, targeting at either minimizing some cost (wasted power or delay) or maximizing some utility (goodput). Our approach relies only on statistical channel knowledge, which reduces the required feedback overhead when compared to other approaches where instantaneous channel knowledge is vital. Numerical results show the effectiveness of the proposed scheme.