While screens at face-to-face bridge tournaments are the exception and require considerable investment in extra equipment and increased effort on the part of the players, the use of "logical screens" on BBO would appear to be simplicity itself:
During the auction, a player should see the calls of his partner and right-hand-opponent simultaneously.
If a player loses network communication (hasn't made a call and can't be pinged - or has been inactive for too long), the same indication of inactivity as now can be shown. But normal hesitations would not be visible to a player's partner, thus eliminating any concerns of unauthorized information.
I'm not suggesting that BITs are a frequent occurrence in BBO-land, but this easy-to-implement method would eliminate them entirely.