We used high-resolution optical HST/WFC3 and multi-conjugate adaptive optics assisted GEMINI GeMS/GSAOI observations in the near-infrared to investigate the physical properties of the globular cluster NGC 6569 in the Galactic bulge. We have obtained the deepest purely NIR color-magnitude diagram published so far for this cluster using ground-based observations, reaching $K_{s}$ $approx$ 21.0 mag (two magnitudes below the main-sequence turn-off point). By combining the two datasets secured at two different epochs, we determined relative proper motions for a large sample of individual stars in the center of NGC 6569, allowing a robust selection of cluster member stars. Our proper motion analysis solidly demonstrates that, despite its relatively high metal content, NGC 6569 hosts some blue horizontal branch stars. A differential reddening map has been derived in the direction of the system, revealing a maximum color excess variation of about $delta E(B-V)$ $sim$ 0.12 mag in the available field of view. The absolute age of NGC 6569 has been determined for the first time. In agreement with the other few bulge globular clusters with available age estimates, NGC 6569 turns out to be old, with an age of about 12.8 Gyr, and a typical uncertainty of 0.8-1.0 Gyr.