I don't believe chess.com has this function. But if you are getting challenges, it means that other people like you for some reason. I don't really consider that a problem! ;)
Anyway, back to your question. Since Chess.com does not have a function, you may have to create something on your behalf.
You could post a note on your profile stating that you are willing to play only bullet chess.
I don't know what type of effect it will have, but surely having such a statement is better than none at all.
Barefoot_Player
I play only bullet (1 min +2sec)... and not other...
How can I prevent the challenges for other (longer) time of game?