Next to H and He, carbon is, together with oxygen, the most abundant element in the Universe and widely used when modelling the formation and evolution of galaxies and their stellar populations. 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. We aim to determine carbon abundances for our sample of 91 microlensed dwarf and subgiant stars in the Galactic bulge. 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. Our 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 six CI lines around 9100{AA}, and oxygen abundances using the three OI lines at about 7770{AA}. One-dimensional (1D) MARCS model stellar atmospheres calculated under the assumption of local thermodynamic equilibrium (LTE) were used, and non-LTE corrections were applied when calculating the synthetic spectra for both C and O. 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, with the exception of a continued decrease in [O/Fe] at super-solar [Fe/H], where other alpha-elements tend to level out. When dividing the bulge sample into two sub-groups, one younger than 8Gyr and one older than 8Gyr, 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 show that the models that best match the data are the ones that have been calculated with the Galactic thin and thick disks in mind. We conclude that carbon, oxygen, and the combination of the two support the idea that the majority of the stars in the Galactic bulge have a secular origin; that is, they are formed from disk material. We cannot exclude that a fraction of stars in the bulge could be classified as a classical bulge population, but it would have to be small. More dedicated and advanced models of the inner region of the Milky Way are needed to make more detailed comparisons to the observations.