There are two classes used by WordPress to display the notification bubbles:
update-plugins
awaiting-mod
Your notifications have nothing to do with plugins, so it will be nicer to use the second class. You should change your function like this:
function contact_form_create() {
$notification_count = 2; // Notification value
add_menu_page(
'Contact Forms',
$notification_count ? sprintf('Contact Forms <span class="awaiting-mod">%d</span>', $notification_count) : 'Contact Forms',
'manage_options',
'contact-form',
'contact_form_page_handler'
);
}
add_action('admin_menu', 'contact_form_create');