I would suggest playing 7 rounds as follows:
(14 7 v 1 10) ( 9 13 v 5 8) (4 2 v 11 6) (12 3)
( 8 1 v 2 11) (10 14 v 6 9) (5 3 v 12 7) (13 4)
( 9 2 v 3 12) (11 8 v 7 10) (6 4 v 13 1) (14 5)
(10 3 v 4 13) (12 9 v 1 11) (7 5 v 14 2) ( 8 6)
(11 4 v 5 14) (13 10 v 2 12) (1 6 v 8 3) ( 9 7)
(12 5 v 6 8) (14 11 v 3 13) (2 7 v 9 4) (10 1)
(13 6 v 7 9) ( 8 12 v 4 14) (3 1 v 10 5) (11 2)
This gives everyone exactly six rounds of play and one bye round. Also no partnerships or opponent pairings are duplicated.
Hope that helps.