The following should work for you and give every player, one bye round, 8 different partners and 16 different opponents.
Hope that helps.
(13 12 v 14 16) (8 1 v 17 11) (5 2 v 6 10) (9 4 v 7 15) (18 3)
(14 13 v 15 17) (9 2 v 18 12) (6 3 v 7 11) (1 5 v 8 16) (10 4)
(15 14 v 16 18) (1 3 v 10 13) (7 4 v 8 12) (2 6 v 9 17) (11 5)
(16 15 v 17 10) (2 4 v 11 14) (8 5 v 9 13) (3 7 v 1 18) (12 6)
(17 16 v 18 11) (3 5 v 12 15) (9 6 v 1 14) (4 8 v 2 10) (13 7)
(18 17 v 10 12) (4 6 v 13 16) (1 7 v 2 15) (5 9 v 3 11) (14 8)
(10 18 v 11 13) (5 7 v 14 17) (2 8 v 3 16) (6 1 v 4 12) (15 9)
(11 10 v 12 14) (6 8 v 15 18) (3 9 v 4 17) (7 2 v 5 13) (16 1)
(12 11 v 13 15) (7 9 v 16 10) (4 1 v 5 18) (8 3 v 6 14) (17 2)