I think the schedule below will work for you.
(A U v J S) (B W v E M) (C V v H P) (D X v K R) (F O v I Q) (G N v L T)
(A X v F N) (B V v I T) (C W v L Q) (D U v G O) (E P v J R) (H M v K S)
(A W v G T) (B M v L R) (C P v I S) (D V v F Q) (E O v K X) (H N v J U)
(A N v K Q) (B X v H S) (C U v E R) (D O v J T) (F P v L W) (G M v I V)
(A P v H X) (B O v G W) (C N v F V) (D M v E U) (I R v L S) (J Q v K T)
(A S v E V) (B T v F U) (C Q v G X) (D R v H W) (I P v K N) (J O v L M)
(A V v D W) (B U v C X) (E T v L P) (F S v K O) (G R v J N) (H Q v I M)
(A T v C R) (B S v D Q) (E W v I N) (F X v J M) (G U v K P) (H V v L O)
(A Q v L U) (B R v K V) (C S v J W) (D T v I X) (E N v H O) (F M v G P)
(A R v I O) (B Q v J P) (C T v K M) (D S v L N) (E X v G V) (F W v H U)
(A O v B P) (C M v D N) (E S v F T) (G Q v H R) (I W v J X) (K U v L V)
(A B v M N) (C D v O P) (E F v Q R) (G H v S T) (I J v U V) (K L v W X)
Everyone should have 12 different partners and oppose all other players at least once.
Kim,
A similar schedule is possible with 20 players, however it is not quite as nice since groups of 4 players meet together twice on the last table (see rounds 1&6, 2&7 etc...)
(C O v I Q) (D P v J R) (E N v G T) (F M v H S) (A K v B L)
(A S v E Q) (B T v F R) (G P v I L) (H O v J K) (C M v D N)
(A N v I R) (B M v J Q) (C K v G S) (D L v H T) (E O v F P)
(A T v C P) (B S v D O) (E M v I K) (F N v J L) (G Q v H R)
(A M v G O) (B N v H P) (C L v E R) (D K v F Q) (I S v J T)
(C R v J O) (D Q v I P) (E S v H N) (F T v G M) (A L v B K)
(A R v F S) (B Q v E T) (G K v J P) (H L v I O) (C N v D M)
(A Q v J N) (B R v I M) (C T v H K) (D S v G L) (E P v F O)
(A O v D T) (B P v C S) (E L v J M) (F K v I N) (G R v H Q)
(A P v H M) (B O v G N) (C Q v F L) (D R v E K) (I T v J S)