Tim, my understanding is that a Bike Route is a signed route, recognised (or at least marked off) by contributors to OSM, which is fundamentally different to a cycleway - a stretch of road or path that is suitable for, or specific to, a bicycle. Trust me, not all "bike routes are created equally! :-)

The best place to get accurate information is the OSM website and their Wiki links.

For example: https://wiki.openstreetmap.org/wiki/Beginners%27_guide

Help Forum: https://help.openstreetmap.org/

Discussion forum: https://community.openstreetmap.org/

I'm slowly working my way through gaining an understanding.

Thanks!  After reading more on OSM forums and guides I think I am going down the correct path (pun intended).  "Bicycle Route" is a Feature type. This Feature Type contains the attributes that indicate whether it's National, Regional, or Local etc.  

So add the feature that is a Bicycle Route, then, in the Paths that are included in the Route, add a relationship to the Route.   It's probably more complicated than that, but I'll keep working at it.

That's enough OSM for the day, I'm going for a ride.

Yes – a signposted bicycle route is mapped in OSM as a “relation”, which is a grouping of the “ways” (paths or roads) you’ve been editing. Here’s an example: https://www.openstreetmap.org/relation/5487292