Driving is an option, but do remember this is southern Italy where things are considerably more chaotic than in the north. I once rented a car in Naples and almost caused an accident by braking for a red light. Also beware that the highways can be narrower and less accomodating to truly high speeds than the ones in the north (especially tricky are the 30-feet merge lanes to get onto the highway). I'm not sure I'd recommend a 240-mile trip by car after such a time in the air. It would certainly be fun, but could take longer than you bargain for.

Your best OW option (other than the LGW flight) is to fly to FCO, then take one of the many AZ flights to Bari. If you want to do *A, go via MUC and take the LH flight down. Other options would be to go via LIN, MXP, VER or VCE.