I've never found a pub in Bognor Regis that I'd particularly recommend or rush to return to myself. However the Dog & Duck sounds worth a look. It began as a micropub in the high street a few years ago, but recently relocated to a disused pub at 3 The Steyne, PO21 1TX. It's close to the sea front, slightly to the west of the pier, i.e. 10-15 minutes walk from the ground.
The Dog & Duck on Untappd
untappd.com
They don't seem to have a website but they do have a Facebook page. It sounds to have retained the micropub feel and ethos, despite now being in a more traditional pub building.
Trains are scheduled to run a normal service from Victoria to Bognor Regis, calling at Clapham Junction and East Croydon. There are still some £7 each way advance fares available for some services from East Dulwich to Bognor Regis, changing at East Croydon. (Yes, East Dulwich actually has train service for a second consecutive Saturday!) If you want the flexibility of an open off peak day return, this is one of the routes where it's much more expensive to book from London than to book from the south coast. You can save a few quid by booking a return from Bognor to London, then using the return portion for the outward journey and vice versa.
With 3 away trips in 7 days plus a dental appointment to pay for, I'm probably going to have to miss this one now unless I miss both the cheaper more local games instead.