The village is served by two railway stations on the Southern network. The nearest is Pulborough (3 miles) and the next closest is Billingshurst (4 miles). Trains on this line run between Southampton and Portsmouth and London Victoria, serving Gatwick Airport on the way. You can download a timetable from Southern's website here. I recommend visiting the 'Pocket Timetable' site where you can download a tailored timetable. However, again BEWARE - there is a caveat about accuracy post 20th May. Because of the disruption and poor service by Southern, it is best to check frequency and times before you travel. The line to Brighton can be accessed at Three Bridges and trains to London Bridge can be boarded there also. Journey time to London is around 1:15 to 1:20. Fares etc can be found at Southern's website along with special on-line deals - tickets once booked can easily be retrieved at the station ticket machine using your credit/debit card and booking reference.
Do be aware, as said, that the train service is poor here and that you cannot reliably 'do' an evening show in London and return by train. The last train is 2235 out of Victoria, although you can travel via Horsham later, currently the latest is a 2314 departure out of St Pancras.
3 bus services run through the village. The timetable for the Route 1 can be downloaded here. The service is hourly during the day M-Sat with a reduced service on Sundays.
*** You can check on the running of the service on this page ***. Enter the Route number (1?) and select the direction for live times. There is also a mobile app.
The Horsham service (74) runs roughly every 2 hours from Storrington, Monday - Saturday but only Tuesdays through the village. On Wednesdays the Chichester service (71) runs once that day through the village, and the Route 100 runs Monday-Friday (NB Not through the village) from Burgess Hill to Horsham via Pulborough Station passing Tescos and Sainsburys stores, and less frequently on Saturdays.