In order to achieve controlled bidirectional quantum teleportation of two qubits, based on tensor analysis, von Neumann and Bell basis measurements, we propose criteria for assessing whether an arbitrary nine-qubit entangled state can be used as quantum channel for controlled bidirectional quantum teleportation. Using such a channel, the controller performs a von Neumann measurement, dividing the initial quantum channel into single, dual, triple and quadruple channel. In order to achieve CBQT of two qubits using the proposed criteria, taking the dual channel as an example, Alice, Bob, and the controller work together, using von Neumann measurement, Bell basis measurements, and finally unitary transformations. we verify the feasibility of the proposed standard and set out a general quantum channel selection method.