Ciao Kevin,
You mentioned 2 double rooms at least, but is there an ideal size you're looking for? Because completely private villas generally will not be that small, they are generally bigger than just a 2 bedroom place, especially if you want them to be fully private with their own pool, no neighbors close by. There are several properties that often have a villa or two on the property, away from the "main" villa which is larger and often either offers rooms or apartments.
I can suggest several of "smaller" size villas, not precisely in the area you are looking for but take a look and see whether the fact that they offer full privacy and fully detached make them interesting to consider.
Villa Corsanello - 4 rooms, sleeps up to 8. This is the closest to the area you're interested in, not far from Pienza. Fully detached, the entire villa to yourself, in May your budget should fit excatly.
Holiday in Tuscany: rental villa near Siena with independent garden and swimming pool, 4 bedrooms and 3 bathrooms.
www.tuscanyaccommodation.com
Miravalle @Incrociata - hosts up to 8 people, completely separate and with own outdoor spaces and pool. The property has the agriturismo/farmhouse at the bottom of the hill, while the private house is further up the hill. You have complete privacy away from the other guests.
The farmhouse Incrociata near Arezzo offers its guests welcoming apartments and two independent holiday homes.
www.tuscanyaccommodation.com
Borgo della Meliana - has apartments but also two smaller villas separate from the apartments, each with 3 bedrooms, one has it's own separate pool. There is also a smaller cottage with its own pool, but only has 2 bedrooms.
The apartments at Borgo della Meliana are tastefully decorated and furnished with antiques to create a welcoming atmosphere. Located in Gambassi Terme, the villa apartments are centrally situated in the Tuscan countryside.
www.tuscanyaccommodation.com
Not knowing how "big" you need to go, I'll also suggest these but they might not be what you need.
Cabbiavoli - the "castle" is fully detached with its own pool. Sleeps up to 12 people, with its 6 bedrooms. Lots of space, own private pool. The property also has apartments, but those are set away on another part of the property. The villa hosted Julia Roberts a few years ago ;-).
Exclusive villa with pool in the heart of Chianti only 30 km from Florence offers you the chance to enjoy a special, unforgettable vacation in Tuscany!
www.tuscanyaccommodation.com
Villa Piaggia - this one is the largest, with 9 bedrooms. It is large, so it assumes more guests.... likely doesn't fit your budget but you never know, May is sort of still low season. Depends how much space you want, you could contact them for precise cost for 4 weeks. It is more central and good for visiting across the region.
Villa Piaggia, located in Montaione near San Gimignano, is an exclusive and elegant villa that can host up to 20 guests. The villa and its swimming pool is surrounded by a large park and vineyards, enjoying a beautiful view over the Tuscan countryside.
www.tuscanyaccommodation.com
Villa di Ulignano - this is a gorgeous estate, for large groups, with 11 bedrooms. That's the main villa, so if you're interested in a smaller property but with the feel of the larger villa, you could look into the "dependance" which has 4 bedrooms and can be rented separately.
This luxury villa near Volterra is offered for exclusive rental and can host up 37 guests. The villa, surrounded by a large garden with outdoor pool, is an ideal location for a vacation with friends or wedding or special event such as family reunion.
www.tuscanyaccommodation.com
Let me know if any of these seem interesting, whether you want more suggestions as you refine your "search" once you've seen some of these. Or let me know whether I've missed the mark completely and you intended something different. I'll try to help you out, the most difficult part is that some of these don't post rates until you contact them and I am not sure how off your budget they are.
