We present the distributions of the geometrical covering factors of the dusty tori (f2) of active galactic nuclei (AGNs) using an X-ray selected complete sample of 227 AGNs drawn from the Bright Ultra-hard XMM-Newton Survey. The AGNs have z from 0.05 to 1.7, 2–10 keV luminosities between 1042 and 1046 erg s‑1, and Compton-thin X-ray absorption. Employing data from UKIDSS, 2MASS, and the Wide-field Infrared Survey Explorer in a previous work, we determined the rest-frame 1–20 μm continuum emission from the torus, which we model here with the clumpy torus models of Nenkova et al. Optically classified type 1 and type 2 AGNs are intrinsically different, with type 2 AGNs having, on average, tori with higher f2 than type 1 AGNs. Nevertheless, ∼20% of type 1 AGNs have tori with large covering factors, while ∼23%–28% of type 2 AGNs have tori with small covering factors. Low f2 are preferred at high AGN luminosities, as postulated by simple receding torus models, although for type 2 AGNs the effect is certainly small. f2 increases with the X-ray column density, which implies that dust extinction and X-ray absorption take place in material that share an overall geometry and most likely belong to the same structure, the putative torus. Based on our results, the viewing angle, AGN luminosity, and also f2 determine the optical appearance of an AGN and control the shape of the rest-frame ∼1–20 μm nuclear continuum emission. Thus, the torus geometrical covering factor is a key ingredient of unification schemes.