The bidirectional relay channel, in which two users communicate with each other through a relay node, is a simple but fundamental and practical network architecture. In this paper, we consider the block fading bidirectional relay channel and propose efficient transmission strategies that exploit the block fading property of the channel. Thereby, we consider a decode-and-forward relay and assume that a direct link between the two users is not present. Our aim is to characterize the long-term achievable rate region and to develop protocols which achieve all points of the obtained rate region. Specifically, in the bidirectional relay channel, there exist six possible transmission modes: four point-to-point modes (user 1-to-relay, user 2-to-relay, relay-to-user 1, relay-to-user 2), a multiple-access mode (both users to the relay), and a broadcast mode (the relay to both users). Most existing protocols assume a fixed schedule for using a subset of the aforementioned transmission modes. Motivated by this limitation, we develop protocols which are not restricted to adhere to a predefined schedule for using the transmission modes. In fact, based on the instantaneous channel state information (CSI) of the involved links, the proposed protocol selects the optimal transmission mode in each time slot to maximize the long-term achievable rate region. Thereby, we consider two different types of transmit power constraints: 1) a joint long-term power constraint for all nodes, and 2) a fixed transmit power for each node. Furthermore, to enable the use of a non-predefined schedule for transmission mode selection, the relay has to be equipped with two buffers for storage of the information received from both users. As data buffering increases the end-to-end delay, we consider both delay-unconstrained and delay-constrained transmission in the paper.