thanks to everybody for your reviews.
Relais La Sommità organize a taxi transfer from Bari APT, Train Station, etc. Brindisi APT, train station etc. To book the services please send an email.
We hired a car from Bari airport (Auto Europe- Magiore) and drove down to Ostuni. It was difficult to find la Sommita at first, so do consider a tom tom. We parked on the roadside, and walked up the narrow winding street to the hotel, and the hotel then provided a courtesy shuttle service to and from the secure parking area, which is just below where the hotel is located. Do not be put off by this reply, as it's worth staying there, very beautiful with panoramic views and 1st class service!
Agreed that it's best to get a car anyway, lots of gorgeous small towns to visit all around!!
Not that i know of but if your landing in either Bari or Lecce you may want to rent a car to drive around the region .
Get an answer from La Sommita Relais staff and past guests.