i think the easiest way to do this would be to edit the template for your theme.
in the webassist/themes folder, open the subfolder for your theme, then go to the Templates folder and open the page.dwt.php template for your theme.
Find the following line of code:
<?php
echo($WASideMenu->Body);
?>
and change it to:
<?php
if (WA_Auth_RulePasses("Logged in to users")){
echo($WASideMenu->Body);
}
?>