Call-a-Bike has historic datasets OpenData on the DeutscheBahn OpenData portal under CC-BY License.
You can use the Flinkster API with providernetwork=2 to access Call-a-Bike live Data. You need to register on developer.deutschebahn.com to get a free, unlimited API Key (Zugangstoken).
Example Request: https://api.deutschebahn.com/flinkster-api-ng/v1/bookingproposals?lat=48.15&lon=11.5&radius=5000&limit=100&providernetwork=2 – You also have to set the Authorization header to Bearer <YOUR-API-KEY>
limit max value is 100, but you can use offset to request moreradius is the searchradius in meters, max value is 10000, min value is 100, default 500,expand to rentalobject,price to get vehicle and price infoThere is also a Documentation PDF (german only), and you can use the API-console (3rd tab)
If you need GBFS, maybe this flinkster2gbfs adapter can help.