Requires Underscore: Ajax dropdown list pattern for bootstrap and lodash. This snippet will fire your ajax event for a dropdown-menu on a text box only after waiting 400 ms for the last input. Afterwards it hooks up a click event to the body to close the dropdown. Yes, I used jquery. No, it isn't required. I personally prefer vanilla javascript.

Silly Bootstrap Ajax Dropdown Code

(function(){
  var debouncedKeyPress;
  function wrapper(e){
    var keycode = e.keyCode||e.which;
    debouncedKeyPress(this);
    if(keycode === 13)//prevent form submission
    {
      e.preventDefault();
      return false;
    } 
  }
  
  function keypress(caller){
    //perform ajax query here
    //$.get(url, callback) have callback fill the ul
    var parent = $(caller).parent('.dropdown');
    var list = parent.find('.dropdown-menu');
    //open the menu
    parent.addClass('open');
    //empty the menu for the callback
    list.html('');
    $('body').click(function(){
      hideMenu(caller);
      $('body').off('click');
    });
  }
  
  function hideMenu(caller){
    //All done, clean up
    var parent = $(caller).parent('.dropdown');
    parent.removeClass('open');
  }
  debouncedKeyPress = _.debounce(keypress, 400);
})()