Traffic in Bari, like in Naples, is well-known as the worst in Italy. Visitors from Central/North Europe and North America will be surprised by the constant misbehaviour of the style of driving. Though, drivers in Bari are trying to take any chance to be the first - which is mostly tolerated by others to a great extend- and even that they pass over red traffic lights (after checking left and right), they are quite careful at the same time. Don't be afraid, but better look twice even in situations that you normally would not expect traffic from that side. Parking in the second, or somtimes even in the third row, especially before bars or a news stand, is also quite common. If you are then blocked (like it happens also to the buses of public transport) it is common use to push the horn. If the people parked their car in such a critical way, they are normally not far away and can be called by the sound of the horn.
The most dangerous vehicles nowadays are scooters. Passing over red traffic lights, and passing on the right side are so common that it seems to be a rule rather than an infringement of traffic regulations. Unfournately, people on bicycles started to take over this bad habits from scooter riders, so it is a good idea to watch also them with special care.