We report radial velocities accurate to ±15 km s-1 for 53 K giants in Baade's window (l = 0°.9, b = -4°), ≈500 pc south of the nucleus. These stars belong to the nuclear bulge population and have abundances derived from low-resolution spectra. The velocity dispersion of the full sample of 53 K giants is 104 ± 10 km s-1; 16 giants with [Fe/H] < -0.3 dex have σ= 126 ± 22 km s-1 and 21 giants with [Fe/H] ≥ 0.3 have σ = 92 ± 14 km s-1. Additional radial velocities accurate to 50 km s-1 for an overlapping sample of 71 bulge K giants show the same dependence of velocity dispersion on abundance. In both samples, the lower velocity dispersion of the metal-rich giants is significant at a level >90%. If the metal-rich K giants actually have a smaller dispersion, we show that the metal-rich K giants are more centrally concentrated and/or rotate more than the metal-poor K giants. The velocity dispersion of the metal-poor K giants is consistent with their belonging to the same r-3.5 spheroid as the globular clusters and RR Lyrae stars. If the metal-rich giants have a rotation velocity of ≈100 km s-1, they follow an r-4.8 density law; if they do not rotate, they are even more concentrated. Existing data support the hypothesis that both late M giants and IRAS bulge sources follow steep density laws like that predicted for the metal-rich K giants. The distinct abundance, space distribution, and kinematics of these populations lend support to the idea that the inner 1 kpc may be a separate "central component" - a high-density region of chemical and dynamical evolution distinct from the spheroid. The abundance distribution of 88 K giants in Baade's window is fitted remarkably well by the simple "closed box" model of chemical evolution with all gas turned into stars, and a yield, 〈z〉 = 2.0 ± 0.3z⊙. The abundance distribution, which is skewed toward the metal-poor end, contradicts chemical evolution models with significant gas infall but allows models with modest gas outflow if our observed 〈z〉 is smaller than the true yield. Because this would conceivably allow bulge populations with a lower mean abundance to fit the functional form of the simple model, the presence of an abundance gradient in the bulge is entirely consistent with the simple model fit to the Baade's window abundance distribution. A review of data on ages and abundances in the bulge population suggests that neither the age distribution nor the abundance distribution is consistent with the bulge having experienced significant star formation, chemical evolution dominated by gas inflow, or accumulation of intermediate-age satellite systems in the last (1-5) × 109 yr.