B
The letter B in the margin of Great Domesday is an abbreviation for the Latin berewica, an outlying dependency of a manor, physically detached but belonging to the lord of the manor. Berewica, often rendered as berewick, is translated as outlier in the Phillimore edition.
This marginal abbreviation is found only in circuit 6, where it was used extensively, along with M, the abbreviation for manor, and S, for soke, translated as jurisdiction in this edition.
For the manorial structure of circuit 6, see F.M. Stenton, Types of manorial structure in the northern Danelaw (1910); and Dawn M. Hadley, The northern Danelaw: its social structure, c.800-1100 (2000).