This is not the correct way to draw a route in osm and I will revert. You don't redraw another way over the existing mapped roads. 
To create a cycleway route relation you just add the existing road, track, cycleway, footway etc segments that have already been mapped by others along the route to the new cycleway relation you make.
You are likely to need to split the existing ways where the route shifts from a roadway to another way occasionally. 
At times you may need to draw a bit of road or track, etc that hasn't been mapped yet if that is part of the route. You may need to draw a small section to transition from a road to another way where there is no formal way that gets no tags but is added to your route because it is a desired way and so there are no gaps in the route. 
I don't use iD  and expect Josm would be much easier to create routes.
Here is an example of the local bike route and notice that 21 members (or bits of way) make up the relation.
https://www.openstreetmap.org/relation/3836967#map=15/-27.60386/153.13519
 