In this study, we undertake a Bayesian optimization of the Hubbard U parameters of wurtzite GaN and InN. The optimized Us are then tested within the Hubbard-corrected local density approximation (LDA+U) approach against standard density functional theory, as well as a hybrid functional (HSE06). We present the electronic band structures of wurtzite GaN, InN, and (1:1) InGaN superlattice. In addition, we demonstrate the outstanding performance of the new parametrization, when computing the internal electric-fields in a series of [InN]1–[GaN]n superlattices (n = 2–5) stacked up along the c-axis.