Old English bendan "to bend a bow, bring into a curved state; confine with a string, fetter," causative of bindan "to bind," from Proto-Germanic base *band- "string, band" (source also of Old Norse benda "to join, strain, strive, bend"), from PIE root *bhendh- "to bind."
Meaning "curve or make crooked" (early 14c.) is via the notion of bending a bow to string it. Intransitive sense of "become curved or crooked" is from late 14c., that of "incline, turn from the straight line" is from 1510s. Figurative meaning "bow, be submissive" is from c. 1400. Cognate with band, bind, bond, and Bund. Related: Bended; bent; bending.