Green’s Dictionary of Slang

bouncing ben n.

also bouncing benny
[? a sceptical view of learning, i.e. a ben n.1 , who ‘bounces’ with their own self-importance]

an intellectual, a learned person.

[[UK]Chester Courant 17 July 3/5: The saddle was won [...] by Mr Spire’s black horse Satan, who beat Capt. Chattes’ chestnut colt Bouncing Ben].
Liverpool Mail 19 May 2/3: One more throughly the slave of the Colonial-office than Bouncing Ben it would not be possible to imagine.
[UK]Hotten Sl. Dict.
Sveneoaks Chron. 26 May 5/5: The defendant who had a spite against him because he had been appointed manager [...] called him by the nickname of ‘Bouncing Ben’.
[US]A.J. Pollock Und. Speaks 12/1: Bouncing Benny, a keen, intelligent man possessing worldly knowledge (knows the ropes).