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In this contribution, we have investigated the bidirectional quantum teleportation (BQT) of single-qubit states using a Bell state influenced by decoherence channels with memory, dephasing and amplitude damping channels. The expressions of the negativity, as a measure of the entanglement remaining in the BQT quantum channel, the teleportation fidelities and the quantum Fisher information are also evaluated. We find that both these last quantities depend on the survival amount of entanglement in the BQT quantum channel, on the decoherence factor and on the correlation degree of the decoherence channel. We show that in the Markovian regime, the Negativity, the teleportation average fidelities and the quantum Fisher information are slightly enhanced by considering the classical channel correlations. Besides, in the non-Markovian regime, these three quantities could be improved for a long period of time.