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Aims. In this work, we aim to make a differential comparison of the neutron-capture and p-process element molybdenum (Mo) in the stellar populations in the local disk(s) and the bulge, focusing on minimising possible systematic effects in the analysis. Methods. The stellar sample consists of 45 bulge and 291 local disk K-giants, observed with high-resolution optical spectra. The abundances are determined by fitting synthetic spectra using the SME-code. The disk sample is separated into thin- and thick-disk components using a combination of abundances and kinematics. The cosmic origin of Mo is investigated and discussed by comparing with previous published abundances of Mo and the neutron-capture elements cerium (Ce) and europium (Eu). Results. We determine reliable Mo abundances for 35 bulge and 282 disk giants with a typical uncertainty of [Mo/Fe]~0.2 and ~0.1 dex for the bulge and disk, respectively. Conclusions. We find that the bulge possibly is enhanced in [Mo/Fe] compared to the thick disk, which we do not observe in either [Ce/Fe] nor [Eu/Fe]. This might suggest a higher past star-formation rate in the bulge, however, since we do not observe the bulge to be enhanced in [Eu/Fe], the origin of the molybdenum enhancement is yet to be constrained. Although, the scatter is large, we may be observing evidence of the p-process contributing to the heavy element production in the chemical evolution of the bulge.