Stern et al.(2012) presented a study of WISE selection of AGN in the 2 deg^2 COSMOS field, finding that a simple criterion W1-W2>=0.8 provides a highly reliable and complete AGN sample for W2<15.05, where the W1 and W2 passbands are centered at 3.4 and 4.6 microns, respectively. Here we extend this study using the larger 9 deg^2 NOAO Deep Wide-Field Survey Bootes field which also has considerably deeper WISE observations than the COSMOS field, and find that this simple color-cut significantly loses reliability at fainter fluxes. We define a modified selection criterion combining the W1-W2 color and the W2 magnitude to provide highly reliable or highly complete AGN samples for fainter WISE sources. In particular, we define a color-magnitude cut that finds 130+/-4 deg^-2 AGN candidates for W2<17.11 with 90% reliability. Using the extensive UV through mid-IR broad-band photometry available in this field, we study the spectral energy distributions of WISE AGN candidates. As expected, the WISE AGN selection is biased towards objects where the AGN dominates the bolometric luminosity output, and that it can identify highly obscured AGN. We study the distribution of reddening in the AGN sample and discuss a formalism to account for sample incompleteness based on the step-wise maximum-likelihood method of Efstathiou et al.(1988). The resulting dust obscuration distributions depend strongly on AGN luminosity, consistent with the trend expected for a Simpson (2005) receding torus. At L_AGN~3x10^44 erg/s, 29+/-7% of AGN are observed as Type 1, while at ~4x10^45 erg/s the fraction is 64+/-13%. The distribution of obscuration values suggests that dust in the torus is present as both a diffuse medium and in optically thick clouds.
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