In Bughouse can you claim a draw if the position on the board repeated three times but the pieces available to place were different? In Bughouse chess can you make a triple occurrence draw claim if the position on the board has been repeated three times but the pieces available to the players to place were different each time?
Not having a governing body for bughouse, the rules are a little informal.

Per the Wikipedia article:


  Depending on (local) rules threefold repetition applies, in which case
  the reserve of pieces is not taken into account.


If you think about it, if the available pieces were taken into account, first, with no scoresheet, it would be really hard to prove, especially at a typically fast time control; and second, the simple mathematical possibilities would probably render any chances of a draw virtually impossible.

So basically, if the house rules allow for a three-fold repetition, it probably has to be just considering what is on the board of just one of the two boards.

So to answer the base question, most people probably play by those rules, and thus, the answer would be "yes, you can claim a draw under those circumstances".