<div class="container">
  <h1>Bootstrap responsive multiselect</h1>
    <div class="row addremove-multiselect">
      <div class="col-lg-5 col-sm-5 col-xs-12">
        <div class="panel panel-default">
          <div class="panel-heading">Available Services</div>
            <div class="panel-body">
            <select id="available-select" class="multiselect available form-control" size="8" multiple="multiple">
                <option value="PO">PO - Pointer Insecticide</option>
                <option value="SAR">SAR - Service call Aeration</option>
                <option value="SC">SC - Service Call Lawn</option>
                <option value="SCM">SCM - Service Call Manager</option>
                <option value="SCP">SCP - Service Call Perimeter</option>
                <option value="SCQ">SCQ - Service Call Mosquito</option>
                <option value="SCS">SCS - Service Call Moles</option>
                <option value="SCT">SCT - Service Call Tree</option>
                <option value="SH">SH - Shepherd Fungicide</option>
            </select>
           </div>
        </div>
      </div>

      <div class="multiselect-controls col-lg-2 col-sm-2 col-xs-12">
        <button type="button" id="rightall" class="rightall btn btn-block"><i class="glyphicon glyphicon-forward"></i></button>
        <button type="button" id="right" class="right btn btn-block"><i class="glyphicon glyphicon-chevron-right"></i></button>
        <button type="button" id="left" class="left btn btn-block"><i class="glyphicon glyphicon-chevron-left"></i></button>
        <button type="button" id="leftall" class="leftall btn btn-block"><i class="glyphicon glyphicon-backward"></i></button>
      </div>

      <div class="col-lg-5 col-sm-5 col-xs-12">
        <div class="panel panel-default">
          <div class="panel-heading">Selected Services</div>
            <div class="panel-body">
              <select id="selected-select" class="multiselect selected form-control" size="8" multiple="multiple">
              </select>
           </div>
        </div>
      </div>
  </div>
</div>
select {
  overflow: auto;
}

.panel-body {
  padding: 0;
}

.form-control {
  border: none;
}
$(function () { 
  
    function moveItems(origin, dest) {
        $(origin).find(':selected').appendTo(dest);
        $(dest).find(':selected').removeAttr("selected");
        $(dest).sort_select_box();
    }

    function moveAllItems(origin, dest) {
        $(origin).children("option:visible").appendTo(dest);
        $(dest).find(':selected').removeAttr("selected");
        $(dest).sort_select_box();
    }

    $('.left').on('click', function () {
        var container = $(this).closest('.addremove-multiselect');
        moveItems($(container).find('select.multiselect.selected'), $(container).find('select.multiselect.available'));
    });

    $('.right').on('click', function () {
        var container = $(this).closest('.addremove-multiselect');
        moveItems($(container).find('select.multiselect.available'), $(container).find('select.multiselect.selected'));
    });

    $('.leftall').on('click', function () {
        var container = $(this).closest('.addremove-multiselect');
        moveAllItems($(container).find('select.multiselect.selected'), $(container).find('select.multiselect.available'));
    });

    $('.rightall').on('click', function () {
        var container = $(this).closest('.addremove-multiselect');
        moveAllItems($(container).find('select.multiselect.available'), $(container).find('select.multiselect.selected'));
    });

    $('select.multiselect.selected').on('dblclick keyup',function(e){
        if(e.which == 13 || e.type == 'dblclick') {
          var container = $(this).closest('.addremove-multiselect');
          moveItems($(container).find('select.multiselect.selected'), $(container).find('select.multiselect.available'));
        }
    });

    $('select.multiselect.available').on('dblclick keyup',function(e){
        if(e.which == 13 || e.type == 'dblclick') {
            var container = $(this).closest('.addremove-multiselect');
            moveItems($(container).find('select.multiselect.available'), $(container).find('select.multiselect.selected'));
        }
    }); 


});

$.fn.sort_select_box = function(){
    // Get options from select box
    var my_options =$(this).children('option');
    // sort alphabetically
    my_options.sort(function(a,b) {
        if (a.text > b.text) return 1;
        else if (a.text < b.text) return -1;
        else return 0
    })
   //replace with sorted my_options;
   $(this).empty().append( my_options );

   // clearing any selections
   $("#"+this.attr('id')+" option").attr('selected', false);
}

External CSS

  1. https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap.min.css

External JavaScript

  1. https://cdnjs.cloudflare.com/ajax/libs/jquery/2.2.2/jquery.min.js