Authorize users of ROLE_QUESTION_MANAGER role to access the question bank page on admin/index
Also add a link called "Question bank" towards that page from the main left menu (first level entry, not as a part of Administration), only for that role. Alternatively (if changing that menu adds too much complexity or requires dB changes) add it to the user profile drop-down menu on the top right corner.
(get inspiration from the Session admin menu if necessary)