In order to realize the single-qutrit state controlled bidirectional quantum teleportation, a protocol was proposed by using the methods of tensor representation and generalized three-dimensional Bell basis measurement. In this protocol, the quantum state of the controller Carol is arbitrary generalized three-dimensional Bell basis. The six-qutrit entangled state was chosen as the initial quantum channel, and the necessary conditions to judge whether any six-qutrit entangled state could be used as quantum channel were given. Based on the necessary conditions, with the aid of the unitary property of the SO(3) group element, a general method for constructing quantum channels was given by selecting its arbitrary two elements as the unitary matrices. Two specific examples were given, in which Alice, Bob and Carol worked together by performing generalized three-demensional Bell basis measurement and corresponding unitary transformation. At last, the exchange of quantum state between Alice and Bob was achieved, which verified the feasibility of the proposed protocol.