Roland,
The minimum is 5 rounds, and I believe the only way you can do it like this:
(A G B H) (C I D J) (E K F L)
(A G C I) (B H F L) (D J E K)
(A G D J) (B H E K) (C I F L)
(A G E K) (B H C I) (D J F L)
(A G F L) (B H D J) (C I E K)
Note that the players are assigned to 6 fixed pairs who always play together in the same foursome (A G), (B H), (C I), etc... So the schedule has all fixed pairs play together exactly once (essentially a 6 team round robin), this means that any two individuals will play together in the same foursome, either once or five times. This does meet your requirement of 'at least once', but perhaps not quite as you were expecting? For longer schedules, and considering the number of times players are together, then 7 rounds are enough for at least once, and at most three times, and 8 rounds are enough for at least twice and at most three times. I could supply examples of these others if you would like.
Ian.