This study considers amplify-and-forward two-way relay networks, where an energy constrained relay node harvests energy from the received radio-frequency signal. Based on time switching receiver, they separate the energy harvesting (EH) phase and the information processing (IP) phase in time. In the EH phase, three practical wireless power transfer policies are proposed: (i) dual-source (DS) power transfer, where both sources transfer power to the relay; (ii) single-fixed-source power transfer, where a fixed source transfers power to the relay; and (iii) single-best-source (SBS) power transfer, where a source with the strongest channel transfers power to the relay. In the IP phase, a new comparative framework of the proposed wireless power transfer policies is presented in two bi-directional relaying protocols, known as multiple access broadcast (MABC) and time division broadcast (TDBC). To characterise the performance of the proposed policies, new analytical expressions are derived for the outage probability, the throughput, and the system energy efficiency. Numerical results corroborate the authors’ analysis and show: (i) the DS policy performs the best in terms of both outage probability and throughput among the proposed policies, (ii) the TDBC protocol achieves lower outage probability than the MABC protocol, and (iii) there exits an optimal value of EH time fraction to maximise the throughput.