WooCommerce - Create a product categories dropdown list in a shortcode

gistfile1.php

<?php

/**
 * WooCommerce Extra Feature
 * --------------------------
 *
 * Register a shortcode that creates a product categories dropdown list
 *
 * Use: [product_categories_dropdown orderby="title" count="0" hierarchical="0"]
 */
add_shortcode( 'product_categories_dropdown', 'woo_product_categories_dropdown' );

function woo_product_categories_dropdown( $atts ) {
	extract( shortcode_atts(array(
		'count'        => '0',
		'hierarchical' => '0',
		'orderby' 	   => ''
	), $atts ) );

	ob_start();

	// Stuck with this until a fix for http://core.trac.wordpress.org/ticket/13258
	wc_product_dropdown_categories( array(
		'orderby'            => ! empty( $orderby ) ? $orderby : 'order',
		'hierarchical'       => $hierarchical,
		'show_uncategorized' => 0,
		'show_counts'        => $count
	) );
	?>
	<script type='text/javascript'>
		/* <![CDATA[ */
		jQuery(function(){
			var product_cat_dropdown = jQuery(".dropdown_product_cat");
			function onProductCatChange() {
				if ( product_cat_dropdown.val() !=='' ) {
					location.href = "<?php echo esc_url( home_url() ); ?>/?product_cat=" +product_cat_dropdown.val();
				}
			}
			product_cat_dropdown.change( onProductCatChange );
		});
	/* ]]> */
	</script>
	<?php
	return ob_get_clean();
}

Hey Mike, thanks for your work on this. One question though ... is there a way to preselect an entry from the list?

@mikejolley, line #22 links to a ticket that was closed more than a year ago. That ticket also affects https://github.com/woothemes/woocommerce/blob/master/includes/widgets/class-wc-widget-product-categories.php#L208
Could you take a look at that?

How can I add an "All products" link to the list? It works but if I want to go back to shop main page there's no link.

My alternative for SEO friendly URLs:

				<script type="text/javascript">
				    <!--
				    var dropdown = document.getElementById("cat");
				    function onCatChange() {
				        if ( dropdown.options[dropdown.selectedIndex].value !=-1 ) {
				            location.href = "<?php echo esc_url( home_url( '/' ) ); ?>produkt-kategorie/"+dropdown.options[dropdown.selectedIndex].value;
				        }
				    }
				    dropdown.onchange = onCatChange;
				    -->
				</script>

Hi! How to remove the counter next to the category?

error 27: 'show_counts' => $count

corect 27: 'show_count' => $count