BASIL (Bayesian Active Spectral-cube Inference and Learning) derives molecular parameter maps from wideband spectral datacubes of chemically rich astrophysical sources. The code fits local thermodynamic equilibrium (LTE) spectral models to estimate excitation temperature, column density, centroid velocity, and line width for many molecular species simultaneously. BaSIL combines stochastic variational inference with an active learning framework that selects the most informative spatial locations in a datacube for model fitting. Gaussian process models then interpolate the results to produce parameter maps across the full field. This approach enables efficient analysis of large spectral datasets and supports studies of molecular abundances and kinematics in star-forming regions.