We present measurements of the fluorine abundance in a Galactic bulge asymptotic giant branch (AGB) star. The measurements were performed using high-resolution K-band spectra obtained with the CRIRES spectrograph, which has been recently installed at ESO's VLT, together with state-of-the-art model atmospheres and synthetic spectra. This represents the first fluorine abundance measurement in a Galactic bulge star, and one of few measurements of this kind in a third dredge-up oxygen-rich AGB star. The F abundance is found to be close to the solar value scaled down to the metallicity of the star, and in agreement with disk giants that are comparable to the bulge giant studied here. The measurement is of astrophysical interest also because the star's mass can be estimated rather accurately (1.4 less than or similar to M/M-circle dot less than or similar to 2.0). AGB nucleosynthesis models predict only a very mild enrichment of F in such low mass AGB stars. Thus, we suggest that the fluorine abundance found in the studied star is representative for the star's natal cloud, and that fluorine must have been produced at a similar level in the bulge and in the disk.