The conductance of single-molecule junctions may be governed by the structure of the molecule in the gap or by the way it bonds with the leads, and the information contained in a Raman spectrum is ideal for examining both. Here we demonstrate that molecule-to-surface bonding may be characterized during electron transport by 'fishing-mode' tip-enhanced Raman spectroscopy (FM-TERS). This technique allows mutually verifiable single-molecule conductance and Raman signals with single-molecule contributions to be acquired simultaneously at room temperature. Density functional theory calculations reveal that the most significant spectral change seen for a gold-4,4'-bipyridine-gold junction results from the deformation of the pyridine ring in contact with the drain electrode at high voltage, and these calculations suggest that a stronger bonding interaction between the molecule and the drain may account for the nonlinear dependence of conductance on bias voltage. FM-TERS will lead to a better understanding of electron-transport processes in molecular junctions.