Old English byrgan "to raise a mound, hide, enclose in a grave or tomb, inter," akin to beorgan "to shelter," from Proto-Germanic *burzjan- "protection, shelter" (source also of Old Saxon bergan, Dutch bergen, Old Norse bjarga, Swedish berga, Old High German bergan "protect, shelter, conceal," German bergen, Gothic bairgan "to save, preserve"), from PIE root *bhergh- (1) "to hide, protect." Meaning "cover, conceal from sight" is from 1711. Related: Buried; burying. Burying-ground "cemetery" attested from 1711. Buried treasure is from 1801.
The Old English -y- was a short "oo" sound, like modern French -u-. Under normal circumstances it transformed into Modern English -i- (in bridge, kiss, listen, sister, etc.), but in bury and a few other words (merry, knell) it retained a Kentish change to "e" that took place in the late Old English period. In the West Midlands, meanwhile, the Old English -y- sound persisted, slightly modified over time, giving the standard modern pronunciation of blush, much, church.