Aims: We present the analysis of the [α/Fe] abundance ratios for a large number of stars at several locations in the Milky Way bulge with the aim of constraining its formation scenario. Methods: We obtained FLAMES-GIRAFFE spectra (R = 22 500) at the ESO Very Large Telescope for 650 bulge red giant branch (RGB) stars and performed spectral synthesis to measure Mg, Ca, Ti, and Si abundances. This sample is composed of 474 giant stars observed in 3 fields along the minor axis of the Galactic bulge and at latitudes b = -4°, b = -6°, b = -12°. Another 176 stars belong to a field containing the globular cluster NGC 6553, located at b = -3° and 5° away from the other three fields along the major axis. Stellar parameters and metallicities for these stars were presented in Zoccali et al. (2008, A&A, 486, 177). We have also re-derived stellar parameters and abundances for the sample of thick and thin disk red giants analyzed in Alves-Brito et al. (2010, A&A, 513, A35). Therefore using a homogeneous abundance database for the bulge, thick and thin disk, we have performed a differential analysis minimizing systematic errors, to compare the formation scenarios of these Galactic components. Results: Our results confirm, with large number statistics, the chemical similarity between the Galactic bulge and thick disk, which are both enhanced in alpha elements when compared to the thin disk. In the same context, we analyze [α/Fe] vs. [Fe/H] trends across different bulge regions. The most metal rich stars, showing low [α/Fe] ratios at b = -4° disappear at higher Galactic latitudes in agreement with the observed metallicity gradient in the bulge. Metal-poor stars ([Fe/H] < -0.2) show a remarkable homogeneity at different bulge locations. Conclusions: We have obtained further constrains for the formation scenario of the Galactic bulge. A metal-poor component chemically indistinguishable from the thick disk hints for a fast and early formation for both the bulge and the thick disk. Such a component shows no variation, neither in abundances nor kinematics, among different bulge regions. A metal-rich component showing low [α/Fe] similar to those of the thin disk disappears at larger latitudes. This allows us to trace a component formed through fast early mergers (classical bulge) and a disk/bar component formed on a more extended timescale. Based on observations collected at the European Southern Observatory, Paranal, Chile (ESO programmes 071.B-0617 and 073.B-0074.Full Table 4 is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/530/A54