The existence of a population of millisecond pulsars (MSPs) in the Galactic bulge is supported, among others, by the Fermi GeV excess, a signal of gamma rays coming from the Galactic center (GC) direction and resembling the cumulative emission of known MSPs. A previous study showed that, while these MSPs are unresolved in gamma rays, some of them could have been detected in past X-ray observations. The authors also identified a large number of MSP candidates among unidentified X-ray sources. By analyzing unpublished radio images, we found interesting radio counterparts to 6 of those candidates, and were granted 20h of observations with the Green Bank Telescope to settle on their nature. We discovered two new MSPs, PSR J1740-2807 and PSR J1740-2805, towards one of our radio/X-ray targets, bringing to 4 the number of highly-dispersed MSPs in the GC direction and probably unveiling the first direct evidence of a bulge MSP population. We propose to carry out regular timing of these pulsar with Parkes, in order to reveal their properties and potentially claim association of PSR J1740-2807 with the original X-ray source. The follow up of these sources will have a major impact on our understanding of the Fermi GeV excess.