Context : Aims : We investigate metallicity and \alpha -element abundance gradients along a Galactic longitude strip , at latitude b \sim - 4 ^ { \circ } , with the aim of providing observational constraints for the structure and origin of the Milky Way bulge . Methods : High resolution ( R \sim 22,500 ) spectra for 400 K giants , in four fields within -4.8 ^ { \circ } \lesssim b \lesssim - 3.4 ^ { \circ } and -10 ^ { \circ } \lesssim l \lesssim + 10 ^ { \circ } , were obtained within the GIRAFFE Inner Bulge Survey ( GIBS ) project . To this sample we added another \sim 400 stars in Baade ’ s Window at ( l,b ) = ( 1 ^ { \circ } , -4 ^ { \circ } ) , observed with the identical instrumental configuration : FLAMES GIRAFFE in Medusa mode with HR13 setup . All target stars lie within the red clump of the bulge color magnitude diagram , thus minimizing contamination from the disc or halo stars . The spectroscopic stellar surface parameters were derived with an automatic method based on the GALA code , while the [ Ca/Fe ] and [ Mg/Fe ] abundances as a function of [ Fe/H ] were derived through a comparison with the synthetic spectra using MOOG . We constructed the metallicity distributions for the entire sample , as well as for each field individually , in order to investigate the presence of gradients or field-to-field variations in the shape of the distributions . Results : The metallicity distributions in the five fields are consistent with being drawn from a single parent population , indicating the absence of a gradient along the major axis of the Galactic bar . The global metallicity distribution is well fitted by two Gaussians . The metal poor component is rather broad , with a mean at < [ Fe / H ] > = -0.31 dex and \sigma = 0.31 dex . The metal-rich one is narrower , with mean < [ Fe / H ] > = +0.26 and \sigma = 0.2 dex . The [ Mg/Fe ] ratio follows a tight trend with [ Fe/H ] , with enhancement with respect to solar in the metal-poor regime , similar to the one observed for giant stars in the local thick disc . [ Ca/Fe ] abundances follow a similar trend , but with a considerably larger scatter than [ Mg/Fe ] . A decrease in [ Mg/Fe ] is observed at [ Fe / H ] = -0.44 dex . This knee is in agreement with our previous bulge study of K-giants along the minor axis , but is 0.1 dex lower in metallicity than the one reported for the Bulge microlensed dwarf and sub-giant stars . We found no variation in \alpha -element abundance distributions between different fields . Conclusions :