Context : Alma Cycle 3 observations serendipitously showed strong absorption from diffuse molecular gas in the Galactic bulge at -200 km s ^ { -1 } < { v } < -140 km s ^ { -1 } toward the compact extragalactic continuum source J1744-3116 at ( l , b ) = -2.13 ^ { o } , -1.00 ^ { o } . Aims : We aimed to test whether molecular gas in the bulge could also be detected toward the three other , sufficiently strong mm-wave continuum sources seen toward the bulge at |b| < 3 ^ { o } . Methods : We took absorption profiles of \mathrm { HCO ^ { + } } ( 1-0 ) , HCN ( 1-0 ) , C _ { 2 } H ( 1-0 ) , CS ( 2-1 ) and H ^ { 13 } CO ^ { + } ( 1-0 ) in ALMA Cycle 4 toward J1713-3418 , J1717-3341 , J1733-3722 and J1744-3116 . Results : Strong molecular absorption from disk gas at | \mbox { v } | \la 30 km s ^ { -1 } was detected in all directions , and absorption from the 3 kpc arm was newly detected toward J1717 and J1744 . However , only the sightline toward J1744 is dominated by molecular gas overall and no other sightlines showed molecular absorption from gas deep inside the bulge . No molecular absorption was detected toward J1717 where H I emission from the bulge was previously known . As observed in \mathrm { HCO ^ { + } } , HCN , C _ { 2 } H and CS , the bulge gas toward J1744 at v < -135 km s ^ { -1 } has chemistry and kinematics like that seen near the Sun and in the Milky Way disk generally . We measured isotopologic ratios N ( \mathrm { HCO ^ { + } } ) /N ( H ^ { 13 } CO ^ { + } ) > 51 ~ { } ( 3 \sigma ) for the bulge gas toward J1744 and 58 \pm 9 and 64 \pm 4 for the disk gas toward J1717 and J1744 , respectively , all well above the value of 20-25 typical of the central molecular zone . Conclusions : The kinematics and chemistry of the bulge gas observed toward J1744 more nearly resemble that of gas in the Milky Way disk than in the central molecular zone .