We present the stellar kinematics across the Galactic bulge and into the disk at positive longitudes from the SDSS-III APOGEE spectroscopic survey of the Milky Way. APOGEE includes extensive coverage of the stellar populations of the bulge along the midplane and near-plane regions. From these data, we have produced kinematic maps of 10,000 stars across longitudes of 0° < l < 65°, and primarily across latitudes of | b| < 5° in the bulge region. The APOGEE data reveal that the bulge is cylindrically rotating across all latitudes and is kinematically hottest at the very center of the bulge, with the smallest gradients in both kinematic and chemical space inside the innermost region (| l,b| ) < (5°, 5°). The results from APOGEE show good agreement with data from other surveys at higher latitudes and a remarkable similarity to the rotation and dispersion maps of barred galaxies viewed edge-on. The thin bar that is reported to be present in the inner disk within a narrow latitude range of | b| < 2° appears to have a corresponding signature in [{Fe}/{{H}}] and [α /{Fe}]. Stars with [{Fe}/{{H}}] >‑0.5 have dispersion and rotation profiles that are similar to that of N-body models of boxy/peanut bulges. There is a smooth kinematic transition from the thin bar and boxy bulge (l,| b| ) < (15°, 12°) out to the disk for stars with [{Fe}/{{H}}] >‑1.0, and the chemodynamics across (l, b) suggests that the stars in the inner Galaxy with [{Fe}/{{H}}] >‑1.0 originate in the disk.