We perform the path-integral bosonization of the recently proposed noncommutative massive Thirring model (NCMT1) [JHEP 0503 (2005) 037]. This model presents two types of current-current interaction terms related to the bi-fundamental representation of the group U(1). Firstly, we address the bosonization of a bi-fundamental free Dirac fermion defined on a noncommutative (NC) euclidean plane ℝθ2. In this case we show that the fermion system is dual to two copies of the NC Wess-Zumino-Novikov- Witten model. Next, we apply the bosonization prescription to the NCMT 1 model living on ℝθ2 and show that this model is equivalent to two-copies of the WZNW model and a two-field potential defined for scalar fields corresponding to the global U(1) × U(1) symmetry plus additional bosonized terms for the four fermion interactions. The bosonic sector resembles to the one proposed by Lechtenfeld et al. [Nucl. Phys. B 705 (2005) 477] as the noncommutative sine-Gordon for a pair of scalar fields. The bosonic and fermionic couplings are related by a strong-weak duality. We show that the couplings of the both sectors for some representations satisfy similar relationships up to relevant re-scalings, thus the NC bi-fundamental couplings are two times the corresponding ones of the NC fundamental (anti-fundamental) and eight times the couplings of the ordinary massive Thirring and sine-Gordon models. © SISSA 2005.