Bournville is served by the cross-city line in Birmingham, with trains on the Redditch-Lichfield line, via Birmingham New Street. It is four stops from New Street, and takes around 15 minutes.
Cadbury World is the obvious attraction, and is a few minutes walk (clearly signposted) from the railway station.
As Bournville was built by Quakers, there are no pubs in the area. Nearby Stirchley is the closest place to drink. Both the Three Horseshoes and The British Oak are within five minutes walk of the train station, in the opposite direction to Cadbury World. the Three Horseshoes is somewhat unsavoury and best avoided. The British Oak is a bette bet, being a large pub with five rooms, and a large beer garden. Food is also served here.