Metal-poor stars in the Galactic halo often show strong enhancements in carbon and/or neutron-capture elements. However, the Galactic bulge is notable for its paucity of these carbon-enhanced metal-poor (CEMP) and/or CH-stars, with only two such objects known to date. This begs the question whether the processes that produced their abundance distribution were governed by a comparable nucleosynthesis in similar stellar sites as for their more numerous counterparts in the halo. Recently, two contenders of these classes of stars were discovered in the bulge, at [Fe/H] = −1.5 and −2.5 dex, both of which show enhancements in [C/Fe] of 0.4 and 1.4 dex (respectively), [Ba/Fe] in excess of 1.3 dex, and also elevated nitrogen. The more metal-poor of the stars can be well matched by standard s-process nucleosynthesis in low-mass asymptotic giant branch (AGB) polluters. The other star shows an abnormally high [Rb/Fe] ratio. Here, we further investigate the origin of the abundance peculiarities in the Rb-rich star by new, detailed measurements of heavy element abundances and by comparing the chemical element ratios of 36 species to several models of neutron-capture nucleosynthesis. The i-process with intermediate neutron densities between those of the slow (s-) and rapid (r)-neutron-capture processes has been previously found to provide good matches of CEMP stars with enhancements in both r- and s-process elements (class CEMP-r/s), rather than invoking a superposition of yields from the respective individual processes. However, the peculiar bulge star is incompatible with a pure i-process from a single ingestion event. Instead, it can, statistically, be better reproduced by more convoluted models accounting for two proton ingestion events, or by an i-process component in combination with s-process nucleosynthesis in low-to-intermediate mass (2–3 M_⊙) AGB stars, indicating multiple polluters. Finally, we discuss the impact of mixing during stellar evolution on the observed abundance peculiarities.