the bac filter will start to die after 4 hours or so.
Not all of it, some of it will feed off the dying ones, if you see what I mean, its an exponential decline, if that makes sense.
However, shouldn't think it would last longer that 12 hours - not too sure how it would survive if you put filter medium in a bag/bucket with either fish food to feed it, or cycling medium/ammonia to start another mini cycle.
may work.
or, speak to an LFS near where you are going and see if they can help you with some cycled media or if you can send them some new media to put in their tanks and get some bacteria for when you arrive at your destination!