early 13c., bounsen "to thump, hit," perhaps from Du. bonzen "to beat, thump," or Low Ger. bunsen, or onomatopoeic; sense probably influenced by bound (v.). Sense of "to bounce like a ball" is from 1510s; the rubber check sense is from 1927. Bouncing "vigorous, big" is from 1570s.
1520s, "a heavy blow," also "a leap, a rebound" from bounce (v.).