panel without IDs
HTML
<link rel="stylesheet" href="http://getbootstrap.com/dist/css/bootstrap.css">
<script src="http://getbootstrap.com/dist/js/bootstrap.js"></script>
<div class="panel-group collapse-all-but-one">
<div class="panel panel-primary panel-collapsible>
<div class="panel-heading">Click me to collapse</div>
<div class="panel-body">I will collaaaaaaapse</div>
</div>
<div class="panel panel-warning panel-collapsible">
<div class="panel-heading">Hey another one</div>
<div class="panel-body">I will close when the other one opens</div>
</div>
</div>
JavaScript
$('.panel-collapse').collapse({toggle: false});
$('body').on('click', '[data-toggle=collapse-next]', function (e) {
e.preventDefault();
// Try to close all of the collapse areas first
var parent_id = $(this).data('parent');
$(parent_id+' .panel-collapse').collapse('hide');
// ...then open just the one we want
var $target = $(this).parents('.panel').find('.panel-collapse');
$target.collapse('toggle');
});