In this paper, a bidirectional wireless information and power transmission model with an energy accumulating relay is studied. To implement wireless information and power transmission simultaneously, a time-switching protocol is adopted. In addition, two energy harvesting (EH) protocols are proposed. In the bidirectional continuous-time EH (BI-CT) protocol, the whole transmission block is divided into two parts: EH and information transmission. In the bidirectional discrete-time EH (BI-DT) protocol, the EH time is either 0 or 1. The relay first harvests energy and then forwards information from the user node to the source node. Notably, the relay node stores energy during poor channel conditions, increasing the energy efficiency. Theoretical analyses on the performance of the two proposed protocols are given. It is found that the throughput efficiency depends on various system parameters, such as the transfer power at the relay, distance between the nodes, noise power, and SNR detection threshold. Furthermore, it is observed that BI-DT outperforms BI-CT when the noise power at the relay is high or the distance between the source and the relay is large.