Filter BP Docs capabilities so that only admins can create new docs.

admins-can-create-bp-docs-only.php

<?php 
function my_docs_create_admins_only( $caps, $cap, $user_id, $args ) {
	if ( 'bp_docs_create' == $cap ) {
		// Only admins can create docs.
		if ( bp_current_user_can( 'bp_moderate' ) ) {
			$caps[] = 'exist';
		} else {
			$caps[] = 'do_not_allow';
		}
	}
	return $caps;
}
add_filter( 'bp_docs_map_meta_caps', 'my_docs_create_admins_only', 10, 4 );