On @Ahriman good answer, I want to add a third method.
- Split the party, not in space, but in time. When you have separate players, and the knowledge obtained by some can influence the rest, but not so much the other way around, you can make first play the latter, and then the former.
In your example, you play first with the buried player. You ask him what is he going to do. He rings the bell. Tell him he doesn't hear anything, or maybe he starts hearing steps, fight sound and that stuff. Tell him what to do next. After a time you are confident enough to know which frequency he is going to pull the string, you have enough information to switch to the other players.
When you are playing with the other players, you know how many times he is going to ring the bell or estimate the frequency of the alarm, so you have all the knowledge needed to play the combat, and the other player could not say he stops ringing the bell.
Of course, this method has its disadvantages. In the first place, the first players don't know anything, but the second do know what's going on. In the example, the players fighting do know it's his friend who is buried ringing the bell (unless you introduce a twist: it's not really his friend who was buried there, his friend could be buried somewhere else, or the player could be knowingly or unknowingly controlling an NPC). So the general advice is: less important information comes first.
A second disadvantage is that you sometimes have to make assumptions about some of the other players actions (e.g.: they're going to fight, or the other players is keeping ringing the bell at the same pace).
But the method has its own advantages too. Most obvious, it's much more comfortable that splitting your group in two rooms, and having to move from one to the another (and in your case it avoids keeping one player bored, whithout being able to do much, and without knowing anything).
Another advantage is using the out of game information to build tension. My Storyteller does this all the time. e.g.:
My character is going to have a meeting with an ambassador of another political faction. First, we play the meeting where I make some important decisions: where and when to meet, how much protection I carry, who knows the meeting is taking place.. and so on.
Then the Storyteller changes to other player, who is infiltrated on that political faction, and he learns they have sent an assassin instead of an ambassador, to learn my secrets and then kill me.
After being told what the other character is going to do with that information, the Storyteller switchs back to me. My character has to keep negociating as he was before, but I as a player know that he is going to try to kill me any moment, if no one comes and warn me. The tension is huge.