This depends on which train you take. There is a quick train that makes a few stops on the way, it gets to Horsham and then splits into a fast train going to Portsmouth (with a stop at Barnham - you then need to change trains, go under the subway to platform 1, that's where the Bognor train gets in).
SO, fast train would take about 1hr 20 mins. The slower train, which stops at every little station along the way is more like 1hr 40 mins up to 2 hrs.