I always cancel immediately when I get a BC "BahnCard" (same day or week), these days usually the trial 25% version (3 months, automatic 1 year subscription if you don't cancel).
It used to be pretty bad but nowadays you can cancel a BahnCard online, I used that service at least three times already during the last two years:
https://fahrkarten.bahn.de/privatkunde/kontakt/kontakt_start... (Choose as subject "Kündigung Ihrer BahnCard [25|50]" - page is English, options text still is German)
How exactly did you communicate with them? My wife had a very nice experience with Bahncard re-subscriptions that she cancelled after the fact.
But even then, you know what you get into when ordering the service. Yes, it is a subscription.
Yeah, and better do not forget to cancel those because the friendly DB automatically prolongs these for another year.
In case you refuse to pay, they send a friendly debt collection service -- Infoscore, which conveniently also acts as a credit rating agency.
If you still refuse to pay, the "independent" law firm Haas & Kollegen, which magically resides in the same building as the "independent" debt collection agency and credit rating agency, will take you to court.
Did I mention that these three entities are totally independent, as required by law?