It is impossible to have a schedule with this balance - since the number of possible pairs of players is odd (435). I have found the schedule below which I think is a reasonable compromise, there are 30 rounds and every player has exactly 2 byes. Each player has 28 different partners, opposing 27 of the other players twice and the remaining 2 players just once.
( 7 8 v 5 13) (11 19 v 3 17) (22 21 v 25 28) (10 20 v 16 9) ( 4 15 v 18 23) (24 6 v 30 14) (29 2 v 27 12) ( 1 26)
( 8 9 v 6 14) (12 20 v 4 18) (23 22 v 26 29) (11 21 v 17 10) ( 5 1 v 19 24) (25 7 v 16 15) (30 3 v 28 13) ( 2 27)
( 9 10 v 7 15) (13 21 v 5 19) (24 23 v 27 30) (12 22 v 18 11) ( 6 2 v 20 25) (26 8 v 17 1) (16 4 v 29 14) ( 3 28)
(10 11 v 8 1) (14 22 v 6 20) (25 24 v 28 16) (13 23 v 19 12) ( 7 3 v 21 26) (27 9 v 18 2) (17 5 v 30 15) ( 4 29)
(11 12 v 9 2) (15 23 v 7 21) (26 25 v 29 17) (14 24 v 20 13) ( 8 4 v 22 27) (28 10 v 19 3) (18 6 v 16 1) ( 5 30)
(12 13 v 10 3) ( 1 24 v 8 22) (27 26 v 30 18) (15 25 v 21 14) ( 9 5 v 23 28) (29 11 v 20 4) (19 7 v 17 2) ( 6 16)
(13 14 v 11 4) ( 2 25 v 9 23) (28 27 v 16 19) ( 1 26 v 22 15) (10 6 v 24 29) (30 12 v 21 5) (20 8 v 18 3) ( 7 17)
(14 15 v 12 5) ( 3 26 v 10 24) (29 28 v 17 20) ( 2 27 v 23 1) (11 7 v 25 30) (16 13 v 22 6) (21 9 v 19 4) ( 8 18)
(15 1 v 13 6) ( 4 27 v 11 25) (30 29 v 18 21) ( 3 28 v 24 2) (12 8 v 26 16) (17 14 v 23 7) (22 10 v 20 5) ( 9 19)
( 1 2 v 14 7) ( 5 28 v 12 26) (16 30 v 19 22) ( 4 29 v 25 3) (13 9 v 27 17) (18 15 v 24 8) (23 11 v 21 6) (10 20)
( 2 3 v 15 8) ( 6 29 v 13 27) (17 16 v 20 23) ( 5 30 v 26 4) (14 10 v 28 18) (19 1 v 25 9) (24 12 v 22 7) (11 21)
( 3 4 v 1 9) ( 7 30 v 14 28) (18 17 v 21 24) ( 6 16 v 27 5) (15 11 v 29 19) (20 2 v 26 10) (25 13 v 23 8) (12 22)
( 4 5 v 2 10) ( 8 16 v 15 29) (19 18 v 22 25) ( 7 17 v 28 6) ( 1 12 v 30 20) (21 3 v 27 11) (26 14 v 24 9) (13 23)
( 5 6 v 3 11) ( 9 17 v 1 30) (20 19 v 23 26) ( 8 18 v 29 7) ( 2 13 v 16 21) (22 4 v 28 12) (27 15 v 25 10) (14 24)
( 6 7 v 4 12) (10 18 v 2 16) (21 20 v 24 27) ( 9 19 v 30 8) ( 3 14 v 17 22) (23 5 v 29 13) (28 1 v 26 11) (15 25)
(27 3 v 4 14) (19 25 v 7 24) (30 11 v 2 22) (10 23 v 6 8) (15 9 v 29 16) ( 1 13 v 20 28) (12 18 v 17 21) ( 5 26)
(28 4 v 5 15) (20 26 v 8 25) (16 12 v 3 23) (11 24 v 7 9) ( 1 10 v 30 17) ( 2 14 v 21 29) (13 19 v 18 22) ( 6 27)
(29 5 v 6 1) (21 27 v 9 26) (17 13 v 4 24) (12 25 v 8 10) ( 2 11 v 16 18) ( 3 15 v 22 30) (14 20 v 19 23) ( 7 28)
(30 6 v 7 2) (22 28 v 10 27) (18 14 v 5 25) (13 26 v 9 11) ( 3 12 v 17 19) ( 4 1 v 23 16) (15 21 v 20 24) ( 8 29)
(16 7 v 8 3) (23 29 v 11 28) (19 15 v 6 26) (14 27 v 10 12) ( 4 13 v 18 20) ( 5 2 v 24 17) ( 1 22 v 21 25) ( 9 30)
(17 8 v 9 4) (24 30 v 12 29) (20 1 v 7 27) (15 28 v 11 13) ( 5 14 v 19 21) ( 6 3 v 25 18) ( 2 23 v 22 26) (10 16)
(18 9 v 10 5) (25 16 v 13 30) (21 2 v 8 28) ( 1 29 v 12 14) ( 6 15 v 20 22) ( 7 4 v 26 19) ( 3 24 v 23 27) (11 17)
(19 10 v 11 6) (26 17 v 14 16) (22 3 v 9 29) ( 2 30 v 13 15) ( 7 1 v 21 23) ( 8 5 v 27 20) ( 4 25 v 24 28) (12 18)
(20 11 v 12 7) (27 18 v 15 17) (23 4 v 10 30) ( 3 16 v 14 1) ( 8 2 v 22 24) ( 9 6 v 28 21) ( 5 26 v 25 29) (13 19)
(21 12 v 13 8) (28 19 v 1 18) (24 5 v 11 16) ( 4 17 v 15 2) ( 9 3 v 23 25) (10 7 v 29 22) ( 6 27 v 26 30) (14 20)
(22 13 v 14 9) (29 20 v 2 19) (25 6 v 12 17) ( 5 18 v 1 3) (10 4 v 24 26) (11 8 v 30 23) ( 7 28 v 27 16) (15 21)
(23 14 v 15 10) (30 21 v 3 20) (26 7 v 13 18) ( 6 19 v 2 4) (11 5 v 25 27) (12 9 v 16 24) ( 8 29 v 28 17) ( 1 22)
(24 15 v 1 11) (16 22 v 4 21) (27 8 v 14 19) ( 7 20 v 3 5) (12 6 v 26 28) (13 10 v 17 25) ( 9 30 v 29 18) ( 2 23)
(25 1 v 2 12) (17 23 v 5 22) (28 9 v 15 20) ( 8 21 v 4 6) (13 7 v 27 29) (14 11 v 18 26) (10 16 v 30 19) ( 3 24)
(26 2 v 3 13) (18 24 v 6 23) (29 10 v 1 21) ( 9 22 v 5 7) (14 8 v 28 30) (15 12 v 19 27) (11 17 v 16 20) ( 4 25)