I have been using bootstrap for a while, and I came across an issue when trying to add a dropdown menu dynamically.
This is the JavaScript that I have:
$
Here is a working jsFiddle: http://jsfiddle.net/szx4Y/85/.
FYI, your jsFiddle didn't work because you didn't include the Bootstrap script file. So if you were doing any testing there that wouldn't have worked.
I changed your code to call $(".dropdown-toggle").dropdown(); immediately after you append your HTML. By calling that method you are setting up the elements to handle all the Bootstrap functionality (click events, etc); there's no reason to call it every time you click your new element.
HTML
Javascript
$(document).ready(function() {
$("#clickHere").click(function(){
$("#appendHere").html("");
});
$('.dropdown-toggle').dropdown();
});
CSS
.dropdown-menu {
float:right;
}