mid-14c., bede "prayer bead," from Old English gebed "prayer," with intensive or collective prefix *ge- + Proto-Germanic *bidam "entreaty" (source also of Middle Dutch bede, Old High German beta, German bitte, Gothic bida "prayer, request"), from PIE *bhedh- "to ask, pray," perhaps from a root meaning "to press, urge," hence "to pray."
Shift in meaning came via rosary beads threaded on a string to count prayers, and in verbal phrases bid one's beads, count one's beads, etc. German cognate Bitte is the usual word for conversational request "please." Compare Spanish cuentas "the beads of a rosary," from contar "to count."
The word is also related to bid (Old English biddan) and Gothic bidjan "to ask, pray." Sense in Modern English was transferred to other small globular bodies, such as "drop of liquid" (1590s), "small knob forming front sight of a gun" (1831, Kentucky slang); hence draw a bead on "take aim at," 1841, U.S. colloquial.