A common search is “How to get to Bungay by train?”
The nearest train station to Bungay is Beccles- Beccles train station is on the line between Lowestoft and Ipswich, as well as providing an easy link to London Liverpool Street. From Beccles there are buses to Bungay (it is only a couple of miles between the two market towns).
If you want to go to Bungay from further North then you should travel down to Peterborough and then change at Norwich. From there you can either get the bus to Beccles or take the train to Lowestoft and then change for Beccles there.