We present a novel Bayesian method, referred to as BLOBBY3D, to infer gas kinematics that mitigates the effects of beam smearing for observations using integral field spectroscopy. The method is robust for regularly rotating galaxies despite substructure in the gas distribution. Modelling the gas substructure within the disc is achieved by using a hierarchical Gaussian mixture model. To account for beam smearing effects, we construct a modelled cube that is then convolved per wavelength slice by the seeing, before calculating the likelihood function. We show that our method can model complex gas substructure including clumps and spiral arms. We also show that kinematic asymmetries can be observed after beam smearing for regularly rotating galaxies with asymmetries only introduced in the spatial distribution of the gas. We present findings for our method applied to a sample of 20 star-forming galaxies from the SAMI Galaxy Survey. We estimate the global H α gas velocity dispersion for our sample to be in the range σ¯v ∼[7, 30] km s−1. The relative difference between our approach and estimates using the single Gaussian component fits per spaxel is σ¯v/σ¯v = −0.29 ± 0.18 for the H α flux-weighted mean velocity dispersion.