How do I retrieve bicycle node data?

I guess you're not familiar with the OSM file format, so please read a bit about tagging first.

I'll try to explain it on programmers level without a background in OSM, if this is wrong, please tell me what level you expect.

Basically, OSM data has 3 primitives: Nodes, Ways and Relations. Nodes just have single geographical coordinates, Ways are an ordered list of nodes, and Relations are a collection of other features (thus Nodes, Ways and other Relations).

Every primitive can have a number of tags to denote what type of feature it is.

For the case you're looking at, nodes have a tag rcn_ref=xx (regional cycling network reference), and the ways between those nodes are part of a relation. The relation is tagged as following:

type=route
route=bicycle
network=rcn
note=xx-yy

You can't trust on the correctness of the "note" tags, so you have to calculate the end nodes by getting all the ways in the relation, combining it to a single line and checking the end nodes of that line.

PS: Note that you don't have to download all data, there are services available where you can just download parts of the data (with the tags you want), see Overpass or XAPI

PS2: the tags with rcn are also used in other countries, where they are normal (long) cycle routes, so no node-networks. So you do have to implement extra checks and provide bounding boxes to be sure you're working with node networks.

PS3: User Polyglot also made relations per cycle node network in Belgium, see this: relation 1726882, if you want information regarding cycle nodes you can also contact him.