Old English borian "to bore through, perforate," from bor "auger," from Proto-Germanic *buron (cf. Old Norse bora, Swedish borra, Old High German boron, Middle Dutch boren, German bohren), from PIE root *bher- (2) "to cut with a sharp point, pierce, bore" (cf. Greek pharao "I plow," Latin forare "to bore, pierce," Old Church Slavonic barjo "to strike, fight," Albanian brime "hole").
The meaning "diameter of a tube" is first recorded 1570s; hence figurative slang full bore (1936) "at maximum speed," from notion of unchoked carburetor on an engine. Sense of "be tiresome or dull" first attested 1768, a vogue word c.1780-81 according to Grose; possibly a figurative extension of "to move forward slowly and persistently," as a boring tool does.