I wouldn't recommend trying to rappel or BASE jump there any other day. It's pretty well locked down from what I understand. Just think about how you'd have to derig or loose your expensive rope, escape via water, etc.
On Bridge Day, they do a background check when you register, there are bomb sniffing dogs, and snipers in the forest. I personally saw one. It's considered a terrorist target, and it was closed down for a while after 9/11.
But, if you wanna do it legally, there is some info here:
https://sites.goog.../vbatsrappellteam/