Bungee? Not that I know of - but I might be wrong? If you're in adventurous mood however, do consider spending time at Rancho Baiguate in the mountains (Jarabacoa). Not only is it a beautiful place up there, they have an fantastic adventure centre. You can go white water rafting, canyoning, moutnain biking, riding and much more. Check them out on the link below. I don't know where you'll be staying but it's about 2,5 hours drive from either Santo Domingo or North Coast (Puerto Plata). Most tour operators will take you there on a one-day trip but you can also go by yourself and stay at the ranch for a couple of days. Believe me - it's FUN!!! And especially the Canyoning will get your adrenaline going... Have a great trip.