There isn't a way to do what you're trying to do with shapefiles. Each shapefile is separate. Route lines and stops can't be combined in the same shapefile. Also there is no way to group a set of layers in the web map.
The only way to do this would be to author a map service that combined your data into a service. I assume that's what's happening in the second map example you posted, but unfortunately, that map is not public and I can't view it. Currently, the only way to author a service is with ArcGIS Server. Shortly, we will allow you to create a service in Esri's cloud, by purchasing a subscription to ArcGIS Online.
Thanks,
Mike