I agree with David's reading of the 1861 census doc - Mary is recorded as coming from Bad(d)ingham, Suffolk. The 'where born' entry appears to have been given some attention i.e. it wasn't familiar to the enumerator, who appears to have checked the spelling (changed an 'e' to an 'a'), and reflected the pronunciation with a double 'd'.
If Mary was from Bedingham, Norfolk, there wouldn't be a need for amendment/annotation. Locals knew the parish - Bungay is the market town - and, by 1861, its accepted spelling. Because it's just off the well-used Norwich road they would know it's the other side of the river which forms the county boundary, and so in Norfolk rather than Suffolk.
That said, Badingham, Suffolk isn't really in the Bungay/Waveney valley orbit - it's much more Framlingham and even Woodbridge, and the main roads from that area lead south and west. But Mary Burrows married James Stone in Haddiscoe, which is actually 8-10 miles beyond Bungay and Mettingham, and not on an obvious route (you have to go either to Beccles or to Bungay to cross the river). As you say, horizons tend to be more limited. Work may have taken James and Mary from Haddiscoe to Mettingham after they married, but what took Mary to Haddiscoe in the first place? Family connections (particularly if her father died when she was a child, as the Badingham records suggest)? Is there any connection with the Burrows family in Haddiscoe at the time, and as David said, what happened to Mary's siblings? That's at least two more problems!
