Get custom side bar on custom post archive page

get_sidebar($name) will load a template sidebar-{$name}.php. If sidebar-{$name}.php does not exist, then it will fallback to loading sidebar.php.

to have your specific sidebar, you can create a file sidebar-bibliography_sidebar.php in your theme with this code :

<?php

if ( is_active_sidebar( 'bibliography_sidebar' ) ) {
    dynamic_sidebar( 'bibliography_sidebar' );
}