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Aims. Stars with strong enhancements of r-process elements are rare and tend to be metal-poor, with generally [Fe/H] <-2 dex and found in the halo. In this work we aim to investigate a candidate r-process enriched bulge star with a relatively high metallicity of -0.65 dex, and compare it with a previously published r-rich candidate star in the bulge. Methods. We reconsider the abundance analysis of a high-resolution optical spectrum of the red-giant star 2MASS J18082459-2548444 and determine its europium (Eu) and molybdenum (Mo) abundance, using stellar parameters from five different previous studies. Applying 2MASS photometry, Gaia astrometry and kinematics, we estimate distance, orbits, and population membership of 2MASS J18082459-2548444 and a previously reported r-enriched star 2MASS J18174532-3353235. Results. We find that 2MASS J18082459-2548444 is a relatively metal rich enriched r-process star that is enhanced in Eu and Mo but not substantially enhanced in s-process elements. It has a high probability of membership in the Galactic bulge based on its distance and orbit. We find that both stars show r-process enhancement with elevated [Eu/Fe]-values, even though 2MASS J18174532-3353235 is 1 dex lower in metallicity. Additionally, we find that 2MASS J18174532-3353235 plausibly has a halo or thick disc origin. Conclusions. We conclude that 2MASS J18082459-2548444 represents the first example of a confirmed r-process enhanced star confined to the inner bulge, possibly a relic from a period of enrichment associated with the formation of the bar.