  We have determined the relation between the AGN luminosities at rest-frame 6
{\mu}m associated to the dusty torus emission and at 2-10 keV energies using a
complete, X-ray flux limited sample of 232 AGN drawn from the Bright Ultra-hard
XMM-Newton Survey. The objects have intrinsic X-ray luminosities between 10^42
and 10^46 erg/s and redshifts from 0.05 to 2.8. The rest-frame 6 {\mu}m
luminosities were computed using data from the Wide-Field Infrared Survey
Explorer and are based on a spectral energy distribution decomposition into AGN
and galaxy emission. The best-fit relationship for the full sample is
consistent with being linear, L_6 {\mu}m $\propto$ L_2-10 keV^0.99$\pm$0.032,
with intrinsic scatter, ~0.35 dex in log L_6 {\mu}m. The L_6 {\mu}m/L_2-10 keV
luminosity ratio is largely independent on the line-of-sight X-ray absorption.
Assuming a constant X-ray bolometric correction, the fraction of AGN bolometric
luminosity reprocessed in the mid-IR decreases weakly, if at all, with the AGN
luminosity, a finding at odds with simple receding torus models. Type 2 AGN
have redder mid-IR continua at rest-frame wavelengths <12 {\mu}m and are
overall ~1.3-2 times fainter at 6 {\mu}m than type 1 AGN at a given X-ray
luminosity. Regardless of whether type 1 and type 2 AGN have the same or
different nuclear dusty toroidal structures, our results imply that the AGN
emission at rest-frame 6 {\mu}m is not isotropic due to self-absorption in the
dusty torus, as predicted by AGN torus models. Thus, AGN surveys at rest-frame
6 {\mu}m are subject to modest dust obscuration biases.
