Margot,

Unfortunately I am not a bridge expert. It seems to me that you could adapt the schedule for 16 golfers in four foursomes for your purposes. The schedule here http://mathcentral.uregina.ca/QQ/database/QQ.09.04/bob6.html has every pair of teams together exactly once after 5 rounds. So if you use that schedule for the first 5 rounds, and then use any 3 rounds from it (maybe after renumbering the teams), then every pair of teams will have played together once or twice. That’s the best possible. If you need to assign positions at the table, then do it randomly the first time through, and switch them up the second time.

Hope this helps.
—Victoria