Just append a div with that class to body, then remove it when you're done:
// Show the backdrop
$('<div class="modal-backdrop"></div>').appendTo(document.body);
// Remove it (later)
$(".modal-backdrop").remove();
Live Example:
$("input").click(function() {_x000D_
var bd = $('<div class="modal-backdrop"></div>');_x000D_
bd.appendTo(document.body);_x000D_
setTimeout(function() {_x000D_
bd.remove();_x000D_
}, 2000);_x000D_
});<link href="//netdna.bootstrapcdn.com/twitter-bootstrap/2.3.2/css/bootstrap-combined.min.css" rel="stylesheet" type="text/css" />_x000D_
<script src="//code.jquery.com/jquery.min.js"></script>_x000D_
<script src="//netdna.bootstrapcdn.com/twitter-bootstrap/2.3.2/js/bootstrap.min.js"></script>_x000D_
<p>Click the button to get the backdrop for two seconds.</p>_x000D_
<input type="button" value="Click Me">