Hopefully, this solution will provide assistance. Instead of using the select element, we can utilize the list item element.
<!DOCTYPE html>
<html>
<head>
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css">
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js"></script>
<style>
.dropdown-submenu {
position: relative;
}
.dropdown-submenu .dropdown-menu {
top: 0;
left: 100%;
margin-top: -1px;
}
.dropdown {
width: 100px;
}
</style>
</head>
<body>
<div class="container">
<div class="dropdown">
<button class="btn btn-default btn-lg dropdown-toggle" type="button" data-toggle="dropdown">Choose a State
<span class="caret"></span>
</button>
<ul class="dropdown-menu">
<li class="dropdown-submenu">
<a class="test" tabindex="-1" href="#">Eastern Cape <span class="caret"></span></a>
<ul class="dropdown-menu">
<li><a tabindex="-1" href="#">Umtata / Mthatha</a></li>
<li><a tabindex="-1" href="#">Willowmore</a></li>
<li><a tabindex="-1" href="#">Willowvale</a></li>
</ul>
</li>
<li class="dropdown-submenu">
<a class="test" tabindex="-1" href="#">Free State <span class="caret"></span></a>
<ul class="dropdown-menu">
<li><a tabindex="-1" href="#">Umtata / Mthatha</a></li>
<li><a tabindex="-1" href="#">Willowmore</a></li>
<li><a tabindex="-1" href="#">Willowvale</a></li>
</ul>
</li>
</ul>
</div>
</div>
<script>
$(document).ready(function(){
$('.dropdown-submenu a.test').on("click", function(e){
$(this).next('ul').toggle();
e.stopPropagation();
e.preventDefault();
});
});
</script>
</body>
</html>