Wireless systems that carry delay-sensitive information (such as speech and/or video signals) typically transmit with fixed data rates, but may occasionally suffer from transmission outages caused by the random nature of the fading channels. If the transmitter has instantaneous channel state information (CSI) available, it can compensate for a significant portion of these outages by utilizing power allocation. In this paper, we consider optimal power allocation for a conventional dual-hop bidirectional decode-and-forward (DF) relaying system with a three-phase transmission protocol. The proposed strategy minimizes the average power consumed by the end nodes and the relay, subject to some maximum allowable system outage probability (OP), or equivalently, minimizes the system OP while meeting average power constraints at the end nodes and the relay. We show that in the proposed power allocation scheme, the end nodes and the relay adjust their output powers to the minimum level required to avoid outages, but will sometimes be silent, in order to conserve power and prolong their lifetimes. For the proposed scheme, the end nodes use the instantaneous CSI of their respective source-relay links and the relay uses the instantaneous CSI of both links.