bore (v.1) Look up bore at Dictionary.com
Old English borian "to bore through, perforate," from bor "auger," from Proto-Germanic *buron (cognates: 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" (cognates: 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 (1785); possibly a figurative extension of "to move forward slowly and persistently," as a boring tool does.
bore (v.2) Look up bore at Dictionary.com
past tense of bear (v.).
bore (n.) Look up bore at Dictionary.com
thing which causes ennui or annoyance, 1778; of persons by 1812; from bore (v.1).
The secret of being a bore is to tell everything. [Voltaire, "Sept Discours en Vers sur l'Homme," 1738]