High-precision asteroseismology has improved estimates of stellar masses, radii, and ages. However, this has revealed inaccuracies in typical assumptions regarding properties such as helium abundance (Y) and the mixing-length theory parameter (α). We applied a hierarchical Bayesian model to a sample of main sequence, low-mass dwarf stars to encode population level information about Y and α. We showed that our method reduced the uncertainties in mass, radius and age to 2.5%, 1.2% and 12% respectively compared to grid-based modelling methods. We also show that through our new method, uncertainties decrease with larger sample sizes. With many more asteroseismic targets expected from PLATO, we expect to further improve our inference of bulk stellar parameters.