Bodipy dyes (difluoroboradiaza-s-indacene) are notable for their high quantum yield, intense fluorescence, strong chemical stability and highly tuneable, sharp absorption wavelength with uniquely small Stokes shift. Aza-Bodipy dyes, resulting from the replacement of the methene carbon atom in the bodipy core with a nitrogen atom, additionally show sizable red-shift of the absorption wavelengths. Electron donor materials for organic photovoltaics has recently emerged as promising application of Aza-Bodipy, due to its strong infra-red absorption. Here we present the results of a combined theoretical and experimental investigation of the adsorption characteristics, electronic structure and bonding geometry of single Aza-Bodipy molecules on Au(111) and Ag(110) surfaces. Density functional theory calculations of the density of states (DOS) and adsorption geometry were found to be in qualitative agreement with local DOS and scanning tunneling spectroscopy measurements with a low-temperature scanning tunneling microscope (STM). The strength of the bonding interaction to the substrate was also calculated, and the mobility of the molecule on the surface was investigated by calculating the energy barrier for translations and rotations which were compared with data obtained from STM manipulations.