You don't necessarily have to move the questions in the questions bank if you just want to use them in a new quiz. By default, all the questions you create go into a question bank for the course, and you can then just add them to any other quizzes in the same course.
If you need to use the questions in a different course, then there are two options. The simpler option is to use the Export option (using Moodle XML format) to get the questions out of one course, and then Import them into the other course. This has the advantage that if you edit the questions to adapt them to the new course, then this does not change things in the old course. (It has the disadvantage that if you need to edit the questions to fix the mistake, there are now two copies to edit.)