The best option I can suggest is to use this schedule:
(17 18 v 7 13) (16 11 v 8 10) ( 5 1 v 3 14) ( 2 12 v 9 6) (15 4)
(18 1 v 8 14) (17 12 v 9 11) ( 6 2 v 4 15) ( 3 13 v 10 7) (16 5)
( 1 2 v 9 15) (18 13 v 10 12) ( 7 3 v 5 16) ( 4 14 v 11 8) (17 6)
( 2 3 v 10 16) ( 1 14 v 11 13) ( 8 4 v 6 17) ( 5 15 v 12 9) (18 7)
( 3 4 v 11 17) ( 2 15 v 12 14) ( 9 5 v 7 18) ( 6 16 v 13 10) ( 1 8)
( 4 5 v 12 18) ( 3 16 v 13 15) (10 6 v 8 1) ( 7 17 v 14 11) ( 2 9)
( 5 6 v 13 1) ( 4 17 v 14 16) (11 7 v 9 2) ( 8 18 v 15 12) ( 3 10)
( 6 7 v 14 2) ( 5 18 v 15 17) (12 8 v 10 3) ( 9 1 v 16 13) ( 4 11)
( 7 8 v 15 3) ( 6 1 v 16 18) (13 9 v 11 4) (10 2 v 17 14) ( 5 12)
( 8 9 v 16 4) ( 7 2 v 17 1) (14 10 v 12 5) (11 3 v 18 15) ( 6 13)
( 9 10 v 17 5) ( 8 3 v 18 2) (15 11 v 13 6) (12 4 v 1 16) ( 7 14)
(10 11 v 18 6) ( 9 4 v 1 3) (16 12 v 14 7) (13 5 v 2 17) ( 8 15)
(11 12 v 1 7) (10 5 v 2 4) (17 13 v 15 8) (14 6 v 3 18) ( 9 16)
(12 13 v 2 8) (11 6 v 3 5) (18 14 v 16 9) (15 7 v 4 1) (10 17)
(13 14 v 3 9) (12 7 v 4 6) ( 1 15 v 17 10) (16 8 v 5 2) (11 18)
(14 15 v 4 10) (13 8 v 5 7) ( 2 16 v 18 11) (17 9 v 6 3) (12 1)
(15 16 v 5 11) (14 9 v 6 8) ( 3 17 v 1 12) (18 10 v 7 4) (13 2)
(16 17 v 6 12) (15 10 v 7 9) ( 4 18 v 2 13) ( 1 11 v 8 5) (14 3)
There are 18 rounds, everyone gets exactly 2 byes and gets to play with 16 different partners. Pairs of players play in opposition either once or twice.
HTH.