From Two Micron All Sky Survey infrared photometry, we find two red clump (RC) populations coexisting in fields toward the Galactic bulge at latitudes vertical bar b vertical bar > 5 degrees.5, ranging over similar to 13 degrees in longitude and 20 degrees in latitude. These RC peaks indicate two stellar populations separated by similar to 2.3 kpc; at (l, b) = (+1, -8) the two RCs are located at 6.5 and 8.8 +/- 0.2 kpc. The double-peaked RC is inconsistent with a tilted bar morphology. Most of our fields show the two RCs at roughly constant distance with longitude, also inconsistent with a tilted bar; however, an underlying bar may be present. Stellar densities in the two RCs change dramatically with longitude: on the positive longitude side the foreground RC is dominant, while the background RC dominates negative longitudes. A line connecting the maxima of the foreground and background populations is tilted to the line of sight by similar to 20 degrees +/- 4 degrees, similar to claims for the tilt of a Galactic bar. The distance between the two RCs decreases toward the Galactic plane; seen edge-on the bulge is X-shaped, resembling some extragalactic bulges and the results of N-body simulations. The center of this X is consistent with the distance to the Galactic center, although better agreement would occur if the bulge is 2-3 Gyr younger than 47 Tuc. Our observations may be understood if the two RC populations emanate, nearly tangentially, from the Galactic bar ends, in a funnel shape. Alternatively, the X, or double funnel, may continue to the Galactic center. From the Sun, this would appear peanut/box shaped, but X-shaped when viewed tangentially.