If I understand this correctly, you just need a one-on-one round robin table for six competitors. Your problem is only five rounds are necessary for six competitors to play everybody else once. You can have a double round robin, but that would only be ten rounds.
In the following table the first named team is home. For the last two rounds, you will have to decide on rematches.
5 or 6 players
Rd: Pairings:
1: 1-6 5-2 4-3
2: 6-4 3-5 2-1
3: 2-6 1-3 5-4
4: 6-5 4-1 3-2
5: 3-6 2-4 1-5
6: 6-1 2-5 3-4
7: 4-6 5-3 1-2
8: 6-2 3-1 4-5
9: 5-6 1-4 2-3
10: 6-3 4-2 5-1
Although there are partners in bridge, these partnerships are not assigned--players form 4 player teams ahead of time. For a match, one pair plays east-west and the other north-south in separate rooms. The hands (called "boards") are kept in special trays which show the assigned "dealer" and vulnerability. When each room has played its boards they are swapped and the teammates play the same hands. The team (if any) that did better on a hand either wins it or wins points based on the difference of the scores.
I created that table
here by requesting reversed "colors" the 2
nd time and renumbered the rounds but just noticed team 3 is home for three rounds while 5 is away for 3 (Rds 4-6) and the end of the first round robin and first round of the 2
nd. Can that be corrected?