Opening dialog () not working

The problem and some confusion of yours (and mine, since I had to study jQuery UI and Bootstrap to respond) is that both Bootstrap and jQuery UI have dialogs / modals. So in your code I was loading Bootstrap but using JavaScript / jQuery code for a jQueryUI dialog.

My answer assumes that you continue to use Bootstrap, and remove some of the code you had that was for the jQuery UI.

So you need to change:

# 1 - add the modal / dialog HTML somewhere on the page, eg

<!-- Modal -->
<div class="modal fade" id="myModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true">
  <div class="modal-dialog">
    <div class="modal-content">
      <div class="modal-header">
        <button type="button" class="close" data-dismiss="modal"><span aria-hidden="true">&times;</span><span class="sr-only">Close</span></button>
        <h4 class="modal-title" id="myModalLabel">Modal title</h4>
      </div>
      <div class="modal-body">
        Tem a certeza?
      </div>
      <div class="modal-footer">
        <button type="button" class="btn btn-default" data-dismiss="modal">Fechar</button>
        <button type="button" class="btn btn-primary">Apagar</button>
      </div>
    </div>
  </div>
</div>

# 2 - Change the HTML of the buttons to have Bootstrap attributes:

data-toggle="modal" data-target="#myModal"

# 3 - change JavaScript to use Bootstrap library way

$('#myModal').on('show.bs.modal', function (event) {
    var button = $(event.relatedTarget) // botão que abriu o modal
    var aRemover = button.closest('tr');
    $('#confirmar').on('click', function () {
        $('#myModal').modal('hide')
        aRemover.fadeOut(500, function () {
            aRemover.remove();
        });
        // aqui pode chamar o seu AJAX
    });
});

$('#myModal').on('hide.bs.modal', function (event) {
    $('#confirmar').off('click');
});

Note that in this case / example I used the suggested HTML in the Bootstrap documentation, and gave an ID the delete button to be more comfortable. The HTML I added is:

<!-- Modal -->
<div class="modal fade" id="myModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true">
    <div class="modal-dialog">
        <div class="modal-content">
            <div class="modal-header">
                <button type="button" class="close" data-dismiss="modal"><span aria-hidden="true">&times;</span><span class="sr-only">Close</span>

                </button>
                 <h4 class="modal-title" id="myModalLabel">Modal title</h4>

            </div>
            <div class="modal-body">Tem a certeza?</div>
            <div class="modal-footer">
                <button type="button" class="btn btn-default" data-dismiss="modal">Fechar</button>
                <button type="button" id="confirmar" class="btn btn-primary">Confirmar</button>
            </div>
        </div>
    </div>
</div>

Q: I saw now that you edited the question to use lists instead of table. Then you need to change:

var aRemover = button.closest('tr');

for

var aRemover = button.closest('li');

Using your basic jsfiddle I made some modifications. I believe I have understood correctly what you want.

I put remove() out of success of AJAX for you to see working, then just put it in back.

Link jsfiddle