1590s, "protuberance caused by a blow;" 1610s as "a dull-sounding, solid blow;" see bump (v.). The dancer's bump and grind attested from 1940. To be like a bump on a log "silent, stupidly inarticulate" is by 1863, American English.
1560s, "to bulge out;" 1610s, "to strike heavily, cause to come into violent contact," perhaps from Scandinavian, probably echoic, if the original sense was "hitting" then of "swelling from being hit." It also has a long association with the obsolete verb bum "make a booming noise." To bump into "meet by chance" is from 1886; to bump off "kill" is by 1908 in underworld slang. Related: Bumped; bumping. Bumpsy (adj.) was old slang for "drunk" (1610s).