Stern et al. (2012ApJ...753...30S, Paper I) presented a study of Wide-field Infrared Survey Explorer (WISE) selection of active galactic nuclei (AGNs) in the 2deg^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{mu}m and 4.6{mu}m, respectively. Here we extend this study using the larger 9deg^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+/-4deg^-2^ AGN candidates for W2<17.11 with 90% reliability. Using the extensive UV through mid-IR broadband photometry available in this field, we study the spectral energy distributions of WISE AGN candidates. We find that, as expected, the WISE AGN selection can identify highly obscured AGNs, but that it is biased toward objects where the AGN dominates the bolometric luminosity output. 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. The resulting dust obscuration distributions depend strongly on AGN luminosity, consistent with the trend expected for a receding torus. At L_AGN_~3x10^44^erg/s, 29%+/-7% of AGNs 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.