Countdown includes events that are set to draft.

You are right. I didn’t expect that tribe_get_events() function (a standard approach to getting events from Events Calendar) allowed unpublished events to pass through. I haven’t found a filter for event (post) status in their documentation.
I can propose a workaround:
Locate includes/helper.php file in Events Calendar Bridge plugin folder. Find code like this (around line 143):

// If no posts let's bail
if ( empty( $posts ) ) {
	continue;
}

and change it to:

// discard unpublished events
$posts = array_filter($posts, function($p) {
	return $p->post_status == 'publish';
});

// If no posts let's bail
if ( empty( $posts ) ) {
	continue;
}

Please, let me know if it works.

Perfect! That fixes it. Thank you for the quick reply!

I have published new plugin version (1.2) with “publish status filter” fix. It is safe to update.