Parts of the National Burial Index are on Findmypast, including entries from Bury St Edmunds. There is a burial for a James Reach in 1841 but he was 48 so too old to be the missing James. Perhaps the one who died in 1841 is the schoolmaster who MollyMay found on the 1841 census. His wife, Elizabeth, had died in 1839: 'Yesterday (Tuesday) after a long and severe affliction, Elizabeth, the wife of Mr. James Reach, schoolmaster, of Southgate-street, in this town.' (Bury & Norwich Post, Wednesday 13 February 1839). It's possible that he is also the James who had married in 1838, which would make this marriage very short-lived. If that's the case it seems likely that the children with him on the 1841 census are from an earlier marriage. Perhaps he's the one who was married to Sarah Elmer?