Classical B emission (Be) stars are fast rotating, near-main-sequence B-type stars. The rotation and the presence of circumstellar discs profoundly modify the observables of active Be stars. Our goal is to infer stellar and disc parameters, as well as distance and interstellar extinction, using the currently most favoured physical models for these objects. We present BeAtlas, a grid of $61\, 600$ non-local thermodynamic equilibrium radiative transfer models for Be stars, calculated with the hdust code. The grid was coupled with a Monte Carlo Markov chain (MCMC) code to sample the posterior distribution. We test our method on two well-studied Be stars, α Eri and β CMi, using photometric, polarimetric, and spectroscopic data as input to the code. We recover literature determinations for most of the parameters of the targets, in particular the mass and age of α Eri, the disc parameters of β CMi, and their distances and inclinations. The main discrepancy is that we estimate lower rotational rates than previous works. We confirm previously detected signs of disc truncation in β CMi and note that its inner disc seems to have a flatter density slope than its outer disc. The correlations between the parameters are complex, further indicating that exploring the entire parameter space simultaneously is a more robust approach, statistically. The combination of BeAtlas and Bayesian-MCMC techniques proves successful, and a powerful new tool for the field: The fundamental parameters of any Be star can now be estimated in a matter of hours or days.