I have made a mistake, when I wrote the message above I still had in mind your original posting about 11 players. If there are only 10 players then the byes can be balanced after every 5 matches. So I think you will be more interested to see a schedule for 15 players, the closest multiple of 5 to 17.
(10 8 v 5 4) ( 3 7 v 2 9) ( 6 1)
( 6 9 v 1 5) ( 4 8 v 3 10) ( 7 2)
( 7 10 v 2 1) ( 5 9 v 4 6) ( 8 3)
( 8 6 v 3 2) ( 1 10 v 5 7) ( 9 4)
( 9 7 v 4 3) ( 2 6 v 1 8) (10 5)
( 4 7 v 2 5) ( 1 6 v 9 10) ( 8 3)
( 5 8 v 3 1) ( 2 7 v 10 6) ( 9 4)
( 1 9 v 4 2) ( 3 8 v 6 7) (10 5)
( 2 10 v 5 3) ( 4 9 v 7 8) ( 6 1)
( 3 6 v 1 4) ( 5 10 v 8 9) ( 7 2)
( 7 3 v 5 1) ( 8 2 v 10 9) ( 6 4)
( 8 4 v 1 2) ( 9 3 v 6 10) ( 7 5)
( 9 5 v 2 3) (10 4 v 7 6) ( 8 1)
(10 1 v 3 4) ( 6 5 v 8 7) ( 9 2)
( 6 2 v 4 5) ( 7 1 v 9 8) (10 3)
Above the 10 players have 3 byes and so they play in 12 matches each. There will be 12 partners and 24 opponents for each player. The schedule is arranged so that each player plays with each other (either as partner or opponent) exactly 4 times each. Most pairs of players partner only once, and so will play in opposition three times. The few pairs who partner each other twice, will play in opposition only twice.