If you don't mind staying 20 kilometres outside of the center of town, look into the neighbourhood of Thorpe St Andrew. It's got 2 available options, such as The Old Rectory and Best Western Plus Oaklands Hotel.
For some alternatives, checkout the Randolph Hotel and the Sprowston Manor Marriott Hotel & Country Club. They are 20 kilometres and 25 kilometres respectively from the main center. Wotif also suggests the Salhouse Lodge and the Colston Hall. The first is 25 kilometres away from the center, while the other is 25 kilometres away.
If you'd like to explore some nearby cities, think about Brampton and Uggeshall. Travel 14 kilometres to the southeast from Bungay and you'll find Brampton. That said, Uggeshall is 16 kilometres to the southeast. Brampton hotels include The Stables and The Coach House. The Angel Inn and White Hart Inn are some of the options in Uggeshall.
Hotels in Bungay start at AU$149 per night. Prices and availability subject to change. Additional terms may apply.