Yours, Etc.: Origins and Uses of 8 Sign-Offs
early 13c., bounsen "to thump, hit," perhaps from Dutch bonzen "to beat, thump," or Low German bunsen, or imitative; sense probably influenced by bound (v.). Sense of "to bounce like a ball" is from 1510s; the rubber check sense is from 1927. Related: Bounced; bouncing.
1520s, "a heavy blow," also "a leap, a rebound" from bounce (v.). In reference to politicians and public opinion polls, by 1996, American English.
To recover; return to action: She had a bad case of flu, but bounced back in two days (1950s+)