Yes, this is the way(s). You can map nicely where the bus (or any other) route enters and exits the roundabout: https://www.openstreetmap.org/relation/2453566#map=18/33.789672/-118.143028
It's not compulsory, it's fine if you leave it as single circular road. But if you edit a bus route with Relatify it will automatically split the roundabouts to segments like this.
Note that route relation such as bus relations are added sometimes with entire roundabout without splitting it, that is also fine but splitting it is also fine and there is no consensus which is preferable
https://wiki.openstreetmap.org/wiki/Tag:junction%3Droundabout