It's private property so you must ask, and likely it's a longshot. That said there are typically two routes to this type of thing, the front door or the side door. Either find who is supposed to be in charge and ask them for formal permission, or find someone who simply has access and get them to help you.
As unlikely as it is, knowing or having a prominent member ask for you can help. Other typical issues include liability and insurance, whether they see you and what you are doing as being respectful of the setting and so on. Monetary donations can sometimes be helpful but can also have the opposite effect if they are taken the wrong way. If you are a known photographer, offering your services for free for other purposes may also help if you follow through.