In general, for use with JavaScript, you should use a filter |escapejs:
var $d = $('{{ value|escapejs }}');
However, as a best practice, you better put {{ form|bootstrap }}in HTML and use JavaScript to just fade in:
<div id="djangoForm" style="display:none">{{ form|bootstrap }}</div>
<script>
$('#addDropdown').click(function() {
$('#dropdownContainer').append($('#djangoForm'));
}
</script>