We characterize for the first time the torus properties of an ultra-hard X-ray (14-195 keV) volume-limited (DL < 40 Mpc) sample of 24 Seyfert (Sy) galaxies (BCS40 sample). The sample was selected from the Swift/BAT nine-month catalogue. We use high angular resolution nuclear infrared (IR) photometry and N-band spectroscopy, the CLUMPY torus models and a Bayesian tool to characterize the properties of the nuclear dust. In the case of the Sy1s, we estimate the accretion disc contribution to the subarcsecond resolution nuclear IR SEDs (˜0.4 arcsec) which is, on average, 46 ± 28, 23 ± 13, and 11 ± 5 per cent in the J, H, and K bands, respectively. This indicates that the accretion disc templates that assume a steep fall for longer wavelengths than 1 μm might underestimate its contribution to the near-IR emission. Using both optical (broad versus narrow lines) and X-ray (unabsorbed versus absorbed) classifications, we compare the global posterior distribution of the torus model parameters. We confirm that Sy2s have larger values of the torus covering factor (CT ˜ 0.95) than Sy1s (CT ˜ 0.65) in our volume-limited Seyfert sample. These findings are independent of whether we use an optical or X-ray classification. We find that the torus covering factor remains essentially constant within the errors in our luminosity range and there is no clear dependence with the Eddington ratio. Finally, we find tentative evidence that even an ultra-hard X-ray selection is missing a significant fraction of highly absorbed type 2 sources with very high covering factor tori.