Curiously I never thought this dilema would be on the web. I think a software that could alternate partners (so all the players are paired with one another in any given time) would be a nice contribution to the bughouse community. As a small group (12-16) we've come up with a manual "system" that tries to do this even if we have odd numbers playing. Let me show you with a simple example of a 5 player setup:
R1: 1-2 ; 3-4 (5 sits out)
R2: 2-3 ; 4-5 (1 sits out)
R3: 1-4 ; 3-5 (2 sits out)
R4: 1-5 ; 2-4 (3 sits out)
R5: 1-3 ; 2-5 (4 sits out)
We've started using this method with a 'more balanced pairing' in mind. Since all players rotate within the field, fixed 'better couples' is no longer possible. This, in theory, gives more chance to the 'lesser skilled' to have a shot at winning a tournament. In a way, it made it more chess-like since the final scoring became individual an not as a team.
The main issue, which I'm trying to clarify, is that the pairing turns out more complex and cumbersome as the field grows. If you follow the system, you'll see that odd pairings with 7, 11, 15... are the least desirable because 3 participants will be waiting/watching. These scenarios need a programming solution to simplify matters.
As a longtime bughouse enthusiast, I'd like to hear any suggestions as how these parameters should be managed/approached. I hope this gives some light to the original question and ignites an ongoing revealing discussion around this amazing chess variant.