Most suitable time control for bughouse chess is bronstein delay. Here is how it works: if the time control used is D seconds delay, then when it becomes a player's turn to move, the clock waits for D seconds before starting to subtract from the player's remaining time. Using this time control, there is usually no point in moving faster than the D period. It has been used on the Czech Open Bughouse Championship for several years already. Besides, there is enough time to tell your opponent's to show their stuff-pieces, without this "incident" significantly altering the game. You cannot say that about the other time controls.
There are several time controls which can be used for bughouse (or chess or any turn-based game):
There are other rather obscure time controls such as hourglass, overtime etc, which are not suitable for bughouse and have never been used for it, so they aren't discussed here.
The question is: how fast can you move? Without significant premove, one can move in 0.5-1s. If someone is quicker, it means they move primarily on opponent's time, which is called premove. It is forbidden, but most of the time it can't be penalized. FICS server allows true premove, which means you make your move without even knowing your opponent's move first. Of course, if your move is then illegal (for example your opponent might unexpectedly drop-check your king), it is canceled and your clock is ticking. If successful, such a move only takes 0.1s. So we can say that whoever premoves successfully more, has the better time, and thus wins the game. This holds true over the real board as well. Since everyone should move as fast as physically possible, thinking is reduced to minimum and the game becomes more physically intensive than one might think. Messy boards, hidden reserve pieces, pieces placed between squares or knocked down are not uncommon. Obviously it becomes even more extreme during the last seconds.
Still, this time control is by far the most popular. It is traditional, the one only possible without digital clocks. Most people don't like experimenting with obscure increments they don't understand. Some also enjoy those speed races.
Here again players need to move as fast as possible, but unlike no increment, it is likely to get unbalanced time situations, where one team member can sit, but the other can't. This situation arises when one board moves faster than the other. This can change the winning side in sitting situations in ways that are hard to calculate, and strike most experienced players as unfair. However unlike no increment, it is not possible to just flag your opponents, so even in the last seconds you can still play bughouse and not just random as-fast-as-possible moves.
There is one significant, rather odd feature attached to the delay time control. If one is attacking, it is advantageous to move as slow as possible, so that you may get pieces from the other board. Well surely not as slow as possible, but as close as possible to the delay period. Similarly you need to move slow when your partner is defending, to deprive your diagonal opponent from getting too many pieces. Because of this oddity it is not recommended to make the period too long, two seconds being recommended maximum. With just two seconds delay, the above described oddity doesn't have significant impact. 3s or longer delay, you need to constantly think about whether to move fast or slow, which is not what you really want – there are many other things to think about in a bughouse game, such as quality of the moves. Besides it can be very frustrating if you lost a game just because you moved too fast – you haven't understood or simply undervalued the peculiarities of long delay. At the Czech Open in the past we moved from 3s to 2s bronstein delay just because of this.
You should now also understand that for example 5+0 time control, very popular in chess, when used in bughouse is in fact faster than 1+2 delay, despite the fact that bughouse game is on average just 30 moves, in contrast to about 60 moves in chess. That is because in zero increment game you really should move as fast as possible, otherwise you get bad time and lose, and it won't save the game that you still have 4:30 on clock, if your opponents just sit it out.
Also note that selected time control doesn't have significant impact on the result of a game. If one is good at bughouse, they can usually handle any time control. Despite the fact that zero increment is the most popular time control, the best bughouse players in the world are not necessarily the fastest. In a position there are good moves and bad moves, time control plays no role here.