Added extra sidebar, appears on site but not showing on Widgets page?

[aspen]

I added an additional sidebar to appear below the right and left sidebars. I created a new file, sidebar_bottom.php and added this to my sidebar.php file to call it:

<?php include(TEMPLATEPATH."/sidebar_bottom.php");?>

It shows up just fine on the site, but how do I get it to show in the "Widgets" area where you drag and drop widgets into the sidebars. For example, right now on the Widgets page it shows the Sidebar Top, Sidebar Bottom Left and Right where you can drop widgets into them, but my new "Sidebar Bottom" is not showing there. My sidebar_bottom.php file is this:

<div id="b_sidebar">

<ul id="b_sidebarwidgeted">

<?php if ( !function_exists('dynamic_sidebar') || !dynamic_sidebar('Sidebar Bottom') ) : ?>

<li id="meta" class="widget">
<h4><?php _e("Admin", 'studiopress'); ?></h4>
<ul>
<?php wp_register(); ?>
<li><?php wp_loginout(); ?></li>
<li><a href="http://www.wordpress.org/">WordPress</a></li>
<?php wp_meta(); ?>
<li><a href="http://validator.w3.org/check?uri=referer">XHTML</a></li>
</ul>
</li>

<?php endif; ?>

</ul>

</div>

Why does it not show in the Widgets area like the others? Is there another file I have to add something to?

Thanks for your help.