Old English bedd "bed, couch, resting place; garden plot," from Proto-Germanic *badja- (source also of Old Frisian, Old Saxon bed, Middle Dutch bedde, Old Norse beðr, Old High German betti, German Bett, Gothic badi "bed"). This is said to mean perhaps "sleeping place dug in the ground," if it is from PIE root *bhedh- "to dig, pierce" (source also of Hittite beda- "to pierce, prick," Greek bothyros "pit," Latin fossa "ditch," Lithuanian bedu, besti "to dig," Breton bez "grave"). But Boutkan doubts this and finds little reason to assume that Germanic peoples "(still) lived under such primitive circumstances that they dug out their places to sleep."
Both the sleeping and gardening senses are found in Old English; the specific application to planting also is found also in Middle High German and is the only sense of Danish bed. The meaning "bottom of a lake, sea, or watercourse" is from 1580s. The geological sense of "a thick layer, stratum" is from 1680s.
Bed and board "in bed and at the table" (early 13c.) was a term in old law applied to conjugal duties of man and wife; it also could mean "meals and lodging, room and board" (mid-15c.). Bed-and-breakfast in reference to overnight accommodations is from 1838; as a noun, in reference to a place offering such, by 1967.