We present a detailed analysis, including photoionization modeling, of the intrinsic absorption in the Seyfert 1 galaxy NGC 4151 using ultraviolet (UV) spectra from the Hubble Space Telescope Space Telescope Imaging Spectrograph and the Far Ultraviolet Spectrographic Explorer obtained 2002 May as part of a set of contemporaneous observations that included Chandra High Energy Transmission Grating Spectrometer spectra. In our analysis of the Chandra spectra, we determined that the X-ray absorption was dominated by two components: a high-ionization absorber, revealed by the presence of H-like and He-like lines of Mg, Si, and S, and a lower ionization absorber, in which inner shell absorption lines from lower ionization species of these elements formed. We identified the latter as the source of the saturated UV lines of O VI, C IV, and N V associated with the absorption feature at a radial velocity of ~-500 km s-1, which we referred to as component D+E. In the present work, we have derived tighter constrains on the line-of-sight covering factors, densities, and radial distances of the absorbers. We confirm the presence of the three subcomponents of D+E described in our previous paper, with line-of-sight covering factors (Clos) ranging from ~0.5 to 0.9, and find evidence for a fourth component, D+Ed, characterized by low ionization and a Clos ~ 0.2. The complexity of the UV absorption in NGC 4151 may be a consequence of the fact that we are viewing the black hole/accretion disk system at a relatively high inclination and, therefore, may be detecting the densest part of the flow. Our deconvolution of the underlying C IV emission indicates that D+E must lie outside the intermediate line region (ILR), hence at a radial distance of ~0.1 pc. We find that the equivalent widths (EWs) of the low-ionization lines associated with D+E varied over the period from 1999 July to 2002 May. Although over part of this time, the variations were correlated with changes in the UV continuum, the drop in the EWs of these lines between 2001 April and 2002 May are suggestive of bulk motion of gas out of our line of sight. Over this period, Clos for the low-ionization absorption lines dropped from ~0.7 to ~0.2. If these lines from these two epochs arose in the same subcomponent, the transverse velocity of the gas is ≈2100 km s-1. This is similar to the constraint on transverse velocity derived from the drop in the X-ray absorbing column between 2000 March and 2002 May. Transverse velocities of this order are consistent with an origin in a rotating disk, at the roughly radial distance we derived for D+E. As we suggested in our previous study, it is likely that the absorption arises in a disk-driven wind.