[jquery] How to Display Selected Item in Bootstrap Button Dropdown Title

Updated for Bootstrap 3.3.4:

This will allow you to have different display text and data value for each element. It will also persist the caret on selection.

JS:

$(".dropdown-menu li a").click(function(){
  $(this).parents(".dropdown").find('.btn').html($(this).text() + ' <span class="caret"></span>');
  $(this).parents(".dropdown").find('.btn').val($(this).data('value'));
});

HTML:

<div class="dropdown">
  <button class="btn btn-default dropdown-toggle" type="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="true">
    Dropdown
    <span class="caret"></span>
  </button>
  <ul class="dropdown-menu" aria-labelledby="dropdownMenu1">
    <li><a href="#" data-value="action">Action</a></li>
    <li><a href="#" data-value="another action">Another action</a></li>
    <li><a href="#" data-value="something else here">Something else here</a></li>
    <li><a href="#" data-value="separated link">Separated link</a></li>
  </ul>
</div>

JS Fiddle Example