There are not a ton of small options. Many of them are rented separately but are part of a larger estate. They are still stand alone and many do still offer privacy but don't limit your search to 1 bedrooms. Some of them still rent comparable to 2 bedrooms and you may find 2 bedroom villas in the same price range so be sure to look at those options as well. We are staying in a 3 bedroom this year even though we only need two. It was the best combination of what we needed and not much more than the 2 bed we normally stay in.
Contact BestofBVI..they are great to work with. Trudi will help you find the best place in your budget and guides you every step of the way including things like car rentals.
You can reach Trudi at Trudi@bestofbvi.com
Let us know what you choose!