A query script for the Open Street Map API explorer at http://overpass-turbo.eu/ to render all the cycle routes in the current map bounding box.

osm_cycle_routes.xml

<query type="relation" into="hr">
  <has-kv k="route" v="bicycle"/>
  <bbox-query {{bbox}}/>
</query>
<query type="way" into="hrp">
  <recurse from="hr" type="relation-way"/>
  <bbox-query {{bbox}}/>
</query>
<union>
  <item set="hr"/>
  <item set="hrp"/>
</union>
<print mode="body" order="quadtile"/>
<recurse from="hrp" type="way-node"/>
<print mode="skeleton" order="quadtile"/>