Assuming that you are talking about the WP Toolbar, not the BuddyBar. (The basics of doing this for the BuddyBar are the same at the BP level, but the details of rendering the content are different.)
It will be instructive to look at how BP itself builds its Notifications dropdown, in bp_members_admin_bar_notifications_menu() (bp-members/bp-members-adminbar.php). It uses the BP function bp_core_get_notifications_for_user() to call up a list of notifications. Here’s the thing about the latter function: Internally, it organizes notifications by type (in order to get counts) before flattening them out again. That means that your strategy would be to build your own version of bp_core_get_notifications_for_user(), borrowing the grouping logic, but then not collapsing all notifications into a single object, but instead returning an object that contains just a certain type of notification (based either on what is called there $notification->component_name or $notification->component_action). Then create new WP Toolbar menus based on the info returned, using exactly the same logic used in bp_members_admin_bar_notifications_menu() but multiplied by three (for Notifications, Messages, and Friend Requests).
I think it would be a reasonable enhancement request for BuddyPress itself that there be a component or action parameter (or both) for bp_core_get_notifications_for_user(). You can leave this request at http://buddypress.trac.wordpress.org if you would like.