Fluorine (F-19) abundances are derived in a sample of six bulge red giants in Baade's window. These giants span a factor of 10 in metallicity, and this is the first study to define the behavior of F-19 with metallicity in the bulge. The bulge results show an increase in F/O with increasing oxygen. This trend overlaps what is found in the disk at comparable metallicities, with the most oxygen-rich bulge target extending the disk trend. The increase in F/O in the disk arises from F-19 synthesis in both asymptotic giant branch (AGB) stars and metal-rich Wolf-Rayet (WR) stars through stellar winds. The lack of an s-process enhancement in the most fluorine-rich bulge giant in this study suggests that WR stars represented a larger contribution than did AGB stars to F-19 production in the bulge, when compared to the disk. If this result for fluorine is combined with the previously published overall decline in the O/Mg abundance ratios in metal-rich bulge stars, it suggests that WR winds played a role in shaping chemical evolution in the bulge. One star in this study exhibits a very low value of F/O while having a large O abundance; this chemical mixture can be understood if this star formed from gas that was enriched by metal-poor core-collapse supernovae, and it may indicate that chemical evolution in the bulge was inhomogeneous.