Found a ways myself. First is adding code in theme functions.php:
function my_add_post_type_to_search( $query ) {
if ( ! is_admin() && $query->is_main_query() && $query->is_search ) {
$query->set('post_type', array('page', 'post', 'bfd_download') );
}
}
add_filter( 'pre_get_posts', 'my_add_post_type_to_search' );
Second is just changing “exclude_from_search” to false in the class-better-file-download-admin.php.
Anyway, probably it’s worth to add an option to enable or disable files appearing in search results.