Several recent studies have demonstrated that the Galactic bulge hosts two components with different mean metallicities, and possibly different spatial distribution and kinematics. As a consequence, both the metallicity distribution and the radial velocity of bulge stars vary across different line of sights. We present here the metallicity distribution function of red clump stars in 26 fields spread across a wide area of the bulge, with special emphasis on fields close to Galactic plane, at latitudes b=-2 and b=-1, that were not explored before. This paper includes new metallicities from a sample of about 5000 K giant stars, observed at spectral resolution R=6500, in the Calcium II Triplet region. They are the main dataset of the GIRAFFE Inner Bulge Survey. As part of the same survey we have previously published results for a sample of about 600 K giant stars, at latitude b=-4 , derived from higher resolution spectra (R=22,500). Results. The combined sample allows us to trace and characterize the metal poor and metal rich bulge populations down to the inner bulge. We present a density map for each of the two components. Contrary to the expectations from previous works, we found the metal poor population to be more centrally concentrated than the metal rich one, and with a more axisymmetric spatial distribution. The metal rich population, on the other hand, is arranged in a boxy distribution, consistent with an edge-on bar. By coupling metallicities and radial velocities we show that the metal poor population has a velocity dispersion that varies rather mildly with latitude. On the contrary, the metal rich population has a low velocity dispersion far from the plane (b=-8.5), but it has a steeper gradient with latitude, becoming higher than the metal poor one in the innermost field (b=-1). [abridged]
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