JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css">
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js"></script>
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.css">
<script src="https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.js"></script>
<!-- Modal -->
<div id="myModal" class="modal fade" role="dialog">
  <div class="modal-dialog">

    <!-- Modal content-->
    <div class="modal-content">
      <div class="modal-header">
        <button type="button" class="close" data-dismiss="modal">&times;</button>
        <h4 class="modal-title">Try to select an option using the arrow keys..</h4>
      </div>
      <div class="modal-body">
        <input id="search"/>
      </div>
      <div class="modal-footer">
        <button type="button" class="btn btn-default" data-dismiss="modal">Close</button>
      </div>
    </div>

  </div>
</div>

CSS

.ui-autocomplete {
  z-index:2147483647;
}

JavaScript

$(function() {
	//Show modal
  $('#myModal').modal('show');
  
  //Set autocomplete
  $('#search' ).autocomplete({
		source: [
      "ActionScript",
      "Bootstrap",
      "C",
      "C++"
    ]
	});
  
  //Trigger autocomplete after some time
  setTimeout(function(){
  	$('#search').val('c').trigger('keydown');
  }, 500);
});