If you hook a bungee cord onto the object can’t you just use the stored elastic energy to propel yourself forward? The whole point of the piggy back is to take some of its kinetic energy as your own velocity it doesn’t matter if you actually land on it or not.
I was imagining eventually landing on the object. Interstellar space is probably not very interesting on its own.
But how much delta-v one can extract from a bungee jump is just as interesting a problem as how do you break from a huge delta-v and no atmosphere. Maybe one can even direct the jump into a useful direction: interstellar body based propulsion.