We show that the bulge and the disk of the Milky Way (MW) at R$lesssim$7~kpc are well described by a unique chemical evolution and a two-phase star-formation history (SFH). We argue that the populations within this inner disk, not the entire disk, are the same, and that the outer Lindblad resonance (OLR) of the bar plays a key role in explaining this uniformity. In our model of a two-phase star formation history, the metallicity, [$alpha$/Fe] and [$alpha$/H] distributions, and age-metallicity relation are all compatible with the observations of both the inner disk and bulge. The dip at [Fe/H]$sim$0 dex seen in the metallicity distributions of the bulge and inner disk reflects the quenching episode in the SFH of the inner MW at age $sim$8 Gyr, and the common evolution of the bulge and inner disk stars. We show that at z$le$1.5, when the MW was starting to quench, transitioning between the end of the $alpha$-enhanced thick disk formation to the start of the thin disk, and yet was still gas rich, the gas accretion rate could not have been significant. The [$alpha$/Fe] abundance ratio before and after this quenching phase would be different, which is not observed. The present analysis suggests that Milky Way history, and in particular at the transition from the thick to the thin disk -- the epoch of the quenching -- must have been driven by a decrease of the star formation efficiency. We argue that the decline in the intensity of gas accretion, the formation of the bar, and the quenching of the SFR at the same epoch may be causally connected thus explaining their temporal coincidence (abridged).
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