Hi,
you can control whether or not to show the alerts through their css classes.
I’m guessing you’ve copyied Buddypresses way of notification alerts to your own template’s custom header, something like this svn.buddypress.org/branches/2.0/bp-notifications/bp-notifications-adminbar.php
0 notifications is governed through the .no-alert class – and whenever more than 1 notification is shown, it’ll have the .alert class.
So you could do something as as simple as writing .no-alert {display:none}
in your css stylesheet.