I remember two different kinds of 'bouncing' here in Scotland, for toddlers rather than infants.
One was when your dad (usually) crossed his legs and baby was positioned on the top foot whilst being held by the hands. A song like 'Hey Jock, my cuddie' was sung with dad's foot bouncing in a regular rhythm -- until the final line 'My cuddie'll gie ye a fright!', which ended with a real up in the air bounce.
The other option was to sit baby across both knees and facing the adult, who was holding the baby by the hands. Bouncing went on throughout the song until the final line, when the knees were separated and the wean 'fell' into the space.

The words (of great literary significance, I have no doubt) were:-
    Hey Jock, my cuddie!
    My cuddie's ower the dyke.
    Hey Jock, my cuddie
    - My cuddie'll gie ye a fright! (cuddie was a horse, ower the dyke was over the wall, and
gie ye a fright was give you a fright.

With the benefit of many years, I can only wonder at my dad's stamina!