In the strong deflection gravitational lensing, given the fact that a black-bounce, traversable wormhole is indistinguishable from a Schwarzschild black hole and is loosely tested by the Event Horizon Telescope, we intensively study its signatures of weak deflection gravitational lensing in light of the tremendous progress made by the new generation of the near-infrared interferometer GRAVITY. After obtaining its observables, which are the positions, magnitudes of brightness, centroid, and differential time delay between the lensed images, we investigate three astrophysical scenarios: an orbiting star lensed by the Galactic Center Sgr A*, a microlensed star in the Galactic bulge, and microlensing by a nearby lens. We find that the measurements of the observables of Sgr A* provide a promising way to test the black-bounce, traversable wormhole spacetime. GRAVITY can resolve the angular separation, the angular difference, and the time delay between the two lensed images by Sgr A*, and it can marginally detect their deviations from those of the Schwarzschild black hole. The brightness difference between the images and its deviation might be measured by a dedicated space telescope. In the near future, we expect that such a spacetime would be more robustly tested with the weak deflection gravitational lensing by further improved and upgraded GRAVITY+.