You can reach the resort by train. The route is available both from Brindisi and Bari. Be sure to choose Lecce as your final destination, as it is the last stop on the Ancona–Bari–Lecce railway line. Trains to Gallipoli are operated by Ferrovie del Sud Est.
The journey to Bari takes from 1 hour 20 minutes to 2 hours, and about 1 hour to Gallipoli.
You can check the detailed train schedule on this website. The ticket price ranges from about 20 to 40 EUR for two people, depending on the route and class.
Of course, you can also take a taxi. It's not cheap, but it's fast and comfortable.
