We have a local compost group (Kompostgruppe) in our neighborhood in Kleinbasel. You have to become a member, and volunteer to help out at the compost place for an hour 1-2 times a year. You can bring your compost every Saturday morning, and in springtime you get earth for free.
From what I understand, there are different groups all over town. You could try mailing to
kompostberatung@bs.ch, maybe they can tell you where you can find the nearest one. Good luck!