får du includeret jquery.js ?? (ikke vist)
får du includeret bootstrap.js ?? (ikke vist)
en hurtig test med dette includeret. (virker)
prøv at ændre $result fra false til true;
<!DOCTYPE html>
<html lang="da">
    <head>
        <meta http-equiv="Content-Type" content="text/html; charset=utf-8" >
        <meta name="viewport" content="width=device-width, initial-scale=1">
        <title>demo</title>
        <!-- 
http://getbootstrap.com/getting-started/ -->
        <!-- Latest compiled and minified CSS -->
        <link rel="stylesheet" href="
https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css" integrity="sha384-BVYiiSIFeK1dGmJRAkycuHAHRg32OmUcww7on3RYdg4Va+PmSTsz/K68vbdEjh4u" crossorigin="anonymous">
        <!-- Optional theme -->
        <link rel="stylesheet" href="
https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap-theme.min.css" integrity="sha384-rHyoN1iRsVXV4nD0JutlnGaslCJuC7uwjduW9SVrLvRYooPp2bWYgmgJQIXwl/Sp" crossorigin="anonymous">
        <style type="text/css">
        </style>
        <script type="text/javascript" src="
http://ajax.googleapis.com/ajax/libs/jquery/1/jquery.min.js"></script>        <!-- Latest compiled and minified JavaScript -->
        <script src="
https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js" integrity="sha384-Tc5IQib027qvyjSMfHjOMaLkfuWVxZxUPnCJA7l2mCWNIpG9mGCD8wGNIcPD7Txa" crossorigin="anonymous"></script>
        <?php        
        // $result = true; // test
        $result = false; // test        
        if ($result) {
            echo "<script type=\"text/javascript\">
            $(function(){
                //instantiate your content as modal
                $('#myModal').modal({
                    //modal options here, like keyboard: false for e.g.
                });
                //show the modal when dom is ready
                $('#myModal').modal('show');
            });
            </script>";
        }
        ?>
    </head>
    <body>
        <div class="modal fade" id="myModal" role="dialog">
            <div class="modal-dialog">
                <!-- Modal content-->
                <div class="modal-content">
                    <div class="modal-header">
                        <button type="button" class="close" data-dismiss="modal">×</button>
                        <h4 class="modal-title">Modal Header</h4>
                    </div>
                    <div class="modal-body">
                        <p>Some text in the modal.</p>
                    </div>
                    <div class="modal-footer">
                        <button type="button" class="btn btn-default" data-dismiss="modal">Close</button>
                    </div>
                </div>
            </div>
        </div>
    </body>
</html>