I think you are all familiar of bungee jumping. It's one of the scariest adventure for me but very exciting. It's good for adults only and not for kids. My last bungee jumping adventure was in France. How about in Aruba?
I did a little searching and I can't find anything mentioning bungee jumping in Aruba. That might be one of the few things that is not offered on the beautiful island.
Parasailing and windsurfing are the two big sports in Aruba. I've been to Aruba a lot and I don't recall seeing or hearing about any bungee jumping sites. I would check with the hotel you're staying at. They can tell you for sure.