We apply the probabilistic hierarchical SN Ia SED model BayeSN to analyse SALT-based simulations of SNe Ia to probe consistency between the two models. This paper is the first cross-comparison of dust inference methods using SALT and BayeSN, of great importance given the history of conflicting conclusions regarding the distributions of host galaxy dust properties between the two. Overall we find that BayeSN is able to accurately recover our simulated SALT inputs, establishing excellent consistency between the two models. When inferring dust parameters with simulated samples including non-Ia contamination, we find that our choice of photometric classifier causes a bias in the inferred dust distribution; this arises because SNe Ia heavily impacted by dust are misclassified as contaminants and excluded. We then apply BayeSN to a sample of SNe from DES5YR to jointly infer host galaxy dust distributions and intrinsic differences on either side of a `mass step' at $10^{10}$ M$\odot$. We find evidence in favour of an intrinsic contribution to the mass step and a considerably smaller difference in $R_V$ distributions than most SALT-based analyses, at most $\Delta\mu_{R_V}=0.72\pm0.26$. We also build on recent results in favour of an environmental-dependence on the secondary maximum of SNe Ia in $i$-band. Twenty days post-peak, we find a offset in intrinsic $i$-band light curve between each mass bin at a significance in excess of $3\sigma$.