CONTEXT: [ABRIDGED]. For the Milky Way bulge, there are currently essentially no measurements of carbon in un-evolved stars, hampering our abilities to properly compare Galactic chemical evolution models to observational data for this still enigmatic stellar population. AIMS: We aim to determine carbon abundances for our sample of 91 microlensed bulge dwarf and subgiant stars. Together with new determinations for oxygen this forms the first statistically significant sample of bulge stars that have C and O abundances measured, and for which the C abundances have not been altered by the nuclear burning processes internal to the stars. METHODS: The analysis is based on high-resolution spectra for a sample of 91 dwarf and subgiant stars that were obtained during microlensing events when the brightnesses of the stars were highly magnified. Carbon abundances were determined through spectral line synthesis of five CI lines around 9100 A, and oxygen abundances using the three OI lines at about 7770 A. [ABRIDGED] RESULTS: Carbon abundances was possible to determine for 70 of the 91 stars in the sample and oxygen abundances for 88 of the 91 stars in the sample. The [C/Fe] ratio evolves essentially in lockstep with [Fe/H], centred around solar values at all [Fe/H]. The [O/Fe]-[Fe/H] trend has an appearance very similar to that observed for other alpha-elements in the bulge, [ABRIDGED]. When dividing the bulge sample into two sub-groups, one younger than 8 Gyr and one older than 8 Gyr, the stars in the two groups follow exactly the elemental abundance trends defined by the solar neighbourhood thin and thick disks, respectively. Comparisons with recent models of Galactic chemical evolution in the [C/O]-[O/H] plane shows that the models that best match the data are the ones that have been calculated with the Galactic thin and thick disks in mind. [ABRIDGED] ....
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