The best way is with Ryanair ..... Copenhagen -Napoli alt. Roma Ciampino. Time about 2, 15 minutes. From Napoli simple transfert to the train station,then with Marino bus to Barletta
From Rome, Terravision to Central Station 5 euros, about 1 hour trip. Then train to Barletta ... express train 3.50 min, regional, and cheap train 6.30 min from EUR 10
Total travel time Barletta Roma Ciampino, between 8 to 12 hours. Roma - Napoli between 6 - 8 hours, Copenhagen - Bologna late train Barletta about 10 hours. Prices with Ryanair are often very cheap if you can choose the days that suit Ryanair ... Email for more info.