We report on the near-infrared matches, drawn from three surveys, to the 1640 unique X-ray sources detected by Chandra in the Galactic Bulge Survey (GBS). This survey targets faint X-ray sources in the bulge, with a particular focus on accreting compact objects. We present all viable counterpart candidates and associate a false alarm probability (FAP) to each near-infrared match in order to identify the most likely counterparts. The FAP takes into account a statistical study involving a chance alignment test, as well as considering the positional accuracy of the individual X-ray sources. We find that although the star density in the bulge is very high, ~90 per cent of our sources have an FAP<10 per cent, indicating that for most X-ray sources, viable near-infrared counterparts candidates can be identified. In addition to the FAP, we provide positional and photometric information for candidate counterparts to ~95 per cent of the GBS X-ray sources. This information in combination with optical photometry, spectroscopy and variability constraints will be crucial to characterize and classify secure counterparts.