jats:titleABSTRACT</jats:title> jats:pTo reduce systematic uncertainties in Type Ia supernova (SN Ia) cosmology, the host galaxy dust law shape parameter, RV, must be accurately constrained. We thus develop a computationally inexpensive pipeline, Bird-Snack, to rapidly infer dust population distributions from optical-near-infrared SN colours at peak brightness, and determine which analysis choices significantly impact the population mean RV inference, $\mu RV$. Our pipeline uses a 2D Gaussian process to measure peak BVriJH apparent magnitudes from SN light curves, and a hierarchical Bayesian model to simultaneously constrain population distributions of intrinsic and dust components. Fitting a low-to-moderate-reddening sample of 65 low-redshift SNe yields $\mu RV=2.61-0.35+0.38$, with $68 per cent(95 per cent)$ posterior upper bounds on the population dispersion, . This result is robust to various analysis choices, including: the model for intrinsic colour variations, fitting the shape hyperparameter of a gamma dust extinction distribution, and cutting the sample based on the availability of data near peak. However, these choices may be important if statistical uncertainties are reduced. With larger near-future optical and near-infrared SN samples, Bird-Snack can be used to better constrain dust distributions, and investigate potential correlations with host galaxy properties. Bird-Snack is publicly available; the modular infrastructure facilitates rapid exploration of custom analysis choices, and quick fits to simulated data sets, for better interpretation of real-data inferences.</jats:p>