The　inversion　symmetry　breaking　in　a　Bernal-stacked　graphene　bilayer,　e.g.,　by　applying　a　perpendicular　electric　field,　can　open　a　band　gap　harboring　the　quantum　valley　Hall　effect.　The　different　valley　Hall　topologies　induced　by　a　spatially　varying　electric　field　lead　to　the　formation　of　a　one-dimensional　topological　conducting　channel,　also　called　the　zero-line　mode　(ZLM),　existing　at　the　zero-field　region.　The　ZLMs　were　theoretically　predicted　by　an　atomic　model　and　experimentally　realized　in　bilayer　graphene.　Although　the　atomic　model　has　been　extensively　utilized　to　investigate　the　electronic　properties　of　ZLMs,　a　comprehensive　ab　initio　study　that　precisely　characterizes　the　critical　condition　of　ZLMs　is　still　lacking.　In　this　paper,　by　employing　first-principles　method,　we　systematically　investigate　the　electronic　properties　in　two　realistic　systems,　i.e.,　bilayer　graphene　with　different　types　of　line　defects　and　with　dual-split　gates.　The　characteristics　of　ZLMs　in　different　systems　are　demonstrated.　Interestingly,　we　find　that　bilayer　graphene　with　a　pentagon-heptagon　type　of　line　defect　is　the　optimal　geometry　to　realize　ZLMs　due　to　its　minimum　critical　device　width　as　well　as　a　lower　formation　energy.　Our　first-principles　study　implements　the　research　gap　between　the　atomic　model　and　the　experimental　realization　of　ZLMs,　and　provides　a　practical　scheme　for　realizing　ZLMs　in　bilayer　graphene　systems.