Hi Ratul,
From your link, I picked up the nodes that have relationships and analysed. Here is my recommendation to achieve your goals.
1. I selected two routes: 9 and 23. Here is the Cypher script that I used:
CREATE (bus:Routes {name: "Routes"})
CREATE (route:RtNbr {id: 9})
CREATE (route2:RtNbr {id: 23})
CREATE (bus)-[:ROUTES]->(route)
CREATE (bus)-[:ROUTES]->(route2)
MERGE (stop20: StopID {id:20})
MERGE (stop21: StopID {id:21})
MERGE (stop109: StopID {id:109})
MERGE (stop111: StopID {id:111})
MERGE (stop48: StopID {id:48})
MERGE (stop113: StopID {id:113})
MERGE (stop110: StopID {id:110})
MERGE (route2)-[:START]->(stop20)
MERGE (stop20)-[:TO]->(stop110)
MERGE (stop110)-[:TO]->(stop111)
MERGE (stop111)-[:TO]->(stop48)
MERGE (route)-[:START]->(stop20)
MERGE (stop20)-[:TO]->(stop21)
MERGE (stop21)-[:TO]->(stop109)
MERGE (stop109)-[:TO]->(stop111)
MERGE (stop111)-[:TO]->(stop48)
MERGE (stop48)-[:TO]->(stop113)
;

2. Shortest path between stop id = 20 and stop id = 38:
MATCH (origin:StopID {id: 20}), (destination:StopID {id: 48}),
path = allShortestPaths((origin)-[:TO*]->(destination))
RETURN path;

Hope this will help you.
Thanks,
-Kamal