Central Bari is compact – a 15-minute walk will take you from Piazza Aldo Moro to the old town. For the ferry terminal, take bus 20 (tickets €1.50) from Piazza Moro.
Street parking is migraine-inducing. There's a large parking area (€1) south of the main port entrance; otherwise, there's a large multi-storey car park between the main train station and the FSE station. Another car park is on Via Zuppetta, opposite Hotel Adria.