The one I stayed at is not offered to the public, you have to be a friend of the owner or have a reference. But there are dozens of others available for a fraction of the resort price, and generally offer a superior experience if you don't care about resort facilities (they range from family homes to palatial extravaganzas built by European CEOs to impress their guests). Most villas come with staff that is resort quality, and can arrange things like a car+driver for $40 instead of the $200 resort price, cook for you if you want or fetch takeaway from Ubud restaurants (handy for suckling pig which has a long line). And if you want privacy, they will disappear.

See for example http://www.vrbo.com/search/keywords:ubud%20bali