“As far as I know, if you want to install BuddyPress you’ve got to have a WordPress MU installation “
No, you do not. You can install BuddyPress on a single WordPRess installation.
If the blogs are all on different server,s then you do not have what is meant by a WordPress network (multisite – what WAS MU) and the multi DB plugin will not help you.
I can’t see any way to do what you want without synching the user tables across everything.