Cycle lane data

This Overpass query will return most cycle lanes in a bounding box. It gets all ways with the cycleway key, then removes anything that is cycleway=no.

From the cycleway wiki page, it looks like some other keys, like cycleway:left and cycleway:right may be used. If you haven't, look through all the tagging on that page and see if you want all of them or just a certain selection.

You could also expand this query to include relations.