  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-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 $R_V$ inference, $\mu_{R_V}$. 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 $\mu_{R_V}=2.61^{+0.38}_{-0.35}$, with $68\%(95\%)$ 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 datasets, for better
interpretation of real-data inferences.
