Forgive me if this is already covered somewhere; I did try searching first...

I have just activated Clubs and I intend to replace my ancient private forums with secondary member groups system.

Is there a way to bulk add members to groups, or is it just by sending out invites through the Club interface?

With a plugin, yes. 

Well, I decided to edit the database directly to do it, except I didn't realise about the club membership cache in the members table... Whoops.