Here we directly probe the electronic properties of bilayer graphene using s-SNOM measurements with a broadly tunable laser source over the energy range from 0.3 to 0.54 eV. We tune an OPO/OPA system around the interband resonance of Bernal stacked bilayer graphene (BLG) and extract amplitude and phase of the scattered light. This enables us to retrieve and reconstruct the complex optical conductivity resonance in BLG around 0.39 eV with nanoscale resolution. Our technique opens the door toward nanoscopic noncontact measurements of the electronic properties in complex hybrid 2D and van der Waals material systems, where scanning tunneling spectroscopy cannot access the decisive layers.