Just FYI: I downloaded bp-business theme last night and was unable to get the custom-sidebar plugin to work with the left sidebar template. Finally, I concluded that there was an error in the functions file (after adding content to every single possible sidebar available in the template).
Line 136 in functions.php looked like this:
'name' => __( 'Left Sidebar', 'bp-business' ),
'id' => 'Left-sidebar',
'description' => 'Left Sidebar',
'before_widget' => '<div id="%1$s" class="widget %2$s">',
'after_widget' => '</div>',
'before_title' => '<h4 class="pagetitle">',
'after_title' => '</h4>'
I changed line 139 to
'id' => 'left-sidebar',
Now all works perfectly. Simple fix you might want to pass on to the Theme author (this is a great theme BTW).