[The Codex][1] makes it seem like you can query for a specific comment by ID, as does the [GenerateWP query generator][2], but I couldn't get it to work with either of those examples. Even looking through the `WP_Comment_Query:query()` code makes it clear that you should be able to pass the ID in the parameters.

That said, using `get_comment()` is your only way to go for now. Here's what can work based on your original code:

    <?php
    /**
     * Get the contents of a single comment by its ID.
     * 
     * @param  int $comment_id The ID of the comment to retrieve.
     * 
     * @return string The comment as a string, if present; null if no comment exists.
     */
    function wpse120039_get_comment_by_id( $comment_id ) {
        $comment = get_comment( intval( $comment_id ) );

        if ( ! empty( $comment ) ) {
            return $comment->comment_content;
        } else {
            return '';
        }
    }

    echo '<p>' . wpse120039_get_comment_by_id( '34' ) . '</p>';



  [1]: http://codex.wordpress.org/Class_Reference/WP_Comment_Query
  [2]: http://generatewp.com/wp_comment_query/