To reduce systematic uncertainties in Type Ia supernova (SN Ia) cosmology, the host galaxy dust law shape parameter, R-V, must be accurately constrained. We thus develop a computationally ine xpensiv e pipeline, (0:sc ) Bird-Snack( /0:sc), 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 R(V )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, sigma R-V < 0 . 92(1 . 96). 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.