The recommended airport is Bari-Palese, see the Bari Airport web site. A shuttle service will be organized from the Bari airport to Martina Franca on June 19th, and from Martina Franca to Bari on June 23rd.
The recommended railway station is Stazione di Bari Centrale, see the Trenitalia online timetable.
There are many roads from Bari to Martina Franca. Three of them are indicated in map1, map2, map3, respectively the fastest one, the shortest one and the sea-side one.
Martina Franca is connected to Bari by trains and bus lines of Ferrovie del Sud-Est. Trains leave every 1-2 hours from Monday to Saturday, from the railway station of Bari Centrale: see the timetable. Buses leave every day from Largo Ignazio Ciaia (200 m from the Bari Centrale railway station) or from Largo Sorrentino/via Capruzzi 174 (50 m from the Bari Centrale railway station) , see the timetable