Understanding the formation of metal-molecule contact at the microscopic level is the key towards controlling and manipulating atomic scale devices. Employing two isomers of bipyridine, $4, 4^prime$ bipyridine and $2, 2^prime$ bipyridine between gold electrodes, here, we investigate the formation of metal-molecule bond by studying charge transport through single molecular junctions using a mechanically controlled break junction technique at room temperature. While both molecules form molecular junctions during the breaking process, closing traces show the formation of molecular junctions unambiguously for $4, 4^prime$ bipyridine via a conductance jump from the tunneling regime, referred as `jump to molecular contact, being absent for $2, 2^prime$ bipyridine. Through statistical analysis of the data, along with, molecular dynamics and first-principles calculations, we establish that contact formation is strongly connected with the molecular structure of the electrodes as well as how the junction is broken during breaking process, providing important insights for using a single-molecule in an electronic device.