That's certainly not a common name, Matthew. Here's what I found on it in *A Dictionary of Surnames* (Hanks & Hodges) -- perhaps the most comprehenive reference work published on surnames in the English-speaking world that are of European derivation:
BURY. English: habitation name or topographic name, ultimately from the dative case *byrig*, of Old English *burh* "fortified place", originally used after a preposition (e.g. Richard atte Bery). As inflections were lost in Middle English, derivatives of the Old English dative replaced the Old English nominative, the word taking forms such as *biri*, *berie*, and *burie*. In Middle English this word acquired two different senses, both of which have given rise to surnames. In late Old English and early Middle English it denoted a fortified manor house, and the surname was used for someone who lived near a manor house or as an occupational name for someone employed in a manor house. The word also came to denote a fortified town, and is therefore a habitation hame from any of vaious places so named. From this sense developed the modern English word *borough*.