Resource allocation for half-duplex bidirectional relaying networks using partial channel state information (CSI) at the transmitters is considered, with an emphasis on the diversity-multiplexing tradeoff (DMT). It is assumed that there is a direct link between the sources. It is shown that decode-and-forward (DF) two-way relaying does not suffer from a diversity loss when the multiplexing gain is high, a significant improvement over the dynamic DF protocol for one-way relaying. In contrast to the case of no direct link, power control with CSI feedback from relay to sources provides strictly better performance over systems without power control. The best DMT is obtained when each source broadcasts CSI to the other nodes in the network, allowing them to partially adapt their transmit powers.