Sky Blue Sofa has written up a very good step-by-step tutorial for allowing different users and groups to access Composer:
http://skybluesofa.com/blog/configuring-concrete5-composer-advanced-permissions/
The method for Best Suite - Core is exactly the same, except that you don't set permissions on /dashboard/composer/write but on /dashboard/composer/write-pm
The page is named "Write (for page managers)" in the site map. It is hidden from the main dashboard page because it should not be accessed directly.
You may also set permissions on the actual Page Manager pages that you create, allowing only certain users and groups to edit different types of pages.