This paper is concerned with the privacy-preserving bidirectional electric power data transmission problem of the smart grid. A privacy-preserving bidirectional data transmission (BDT) protocol is developed over semi-quantum computation with aim to achieve bidirectional sensitive data flow between power suppliers and users. The minimal quantum cost is pursued under practical constraints while ensuring that power sensitive information is not leaked. To achieve the goal, a two-way data transmission protocol is first proposed that combines mutual identity authentication with message authentication for the benefits of enhanced security. Furthermore, for the preservation of privacy, a semi-quantum duplex communication approach is utilized, wherein the quantum state is randomly divided into two parts: teleportation and measurement qubits. The effectiveness of the privacy-preserving scheme against existing attack strategies is also rigorously analyzed. Lastly, simulation studies conducted on the IBM quantum cloud platform validate and underscore the superiority of the developed privacy-preserving BDT protocol.