In order to hide an old Blackboard course, please follow the steps below:
In the My Courses box located in the upper right corner of the page click on the gear icon in the upper right corner.
In the Edit Course List menu, find the course(s) you would like to hide.
Once you have located the course(s) that you are hiding, uncheck the Course Name and Announcements fields. Also make sure that the Course ID, Instructors, and Tasks fields are also unchecked.
Click Submit in the upper right corner.
Those courses should no longer appear in the class list on Blackboard. If they still appear, you may want to try logging out and logging back in to Blackboard.