The Milky Way bulge bar is composed of multiple populations. Using chemical and kinematical planes, we segregate six populations in a bulge bar sample observed by the APOGEE survey: two with bar-driven orbits, two with eccentric orbits, and two with low-eccentricity orbits, each composed of low- and high-[Mg/Fe] stars. Our sample spans −2.0 ≲ [Fe/H] ≲ +0.5 and Galactocentric distance RGal < 6 kpc. We use chemical abundances from APOGEE DR17 for the elements Mg, Si, Ca, Al, K, Mn, Co, Ni, and Fe and from the BAWLAS catalog for Ce and Nd. We find that the low- and high-[Mg/Fe] stars with low-eccentricity orbits, which exhibit chemical and orbital characteristics similar to those of the low- and high-[α/Fe] disks, display slightly negative and positive metallicity gradients, respectively. This result for the low-[Mg/Fe], low-eccentricity stars indicates a break in the global thin-disk metallicity gradient. The high-eccentricity populations with both low and high [Mg/Fe] show approximately flat metallicity gradients. In general, the [X/H] gradients of all elements for all populations follow Fe, except for the neutron-capture elements Ce and Nd. For all elements, the high-[Mg/Fe] bar population shows a much steeper positive [X/H] gradient than the nearly flat gradient for the low-[Mg/Fe] bar stars. The positive [X/H] gradients observed among our high-[Mg/Fe] bar stars probably reflect an age variation along the peanut structure. This interpretation agrees with the N-body simulations. Such steep positive gradients have also been reported in some high-redshift (z ∼ 4─10) galaxies.