I can see several issues with your design. The motor control is just one.
Gearing. For 1-3 bounces per second, that's 60-180 RPM. Your motor probably goes something like 1750 RPM. As jsotola commented, you'll need to add a gearbox, or else replace the motor with one that has an integrated gearbox ("gear motor"). You won't be able to reliably control a motor at less than 1/10 its rated speed -- it'll stall, or groan but not move, depending on how you hold your mouth when turning the knob :-).
Resonance. If the weight is to be oscillating on the spring, your system will have a natural frequency. Making the weight heavier, or using a longer or wimpier spring will be slower oscillation; lighter weight or stiffer/shorter spring will be faster. You should plan on experimenting with springs to get the right bounce speed.
The up-and-down drive from the motor should match the mechanical resonance. Adjusting motor speed to drive it off-resonance will still sort of work, but not nearly as well. If you really want variable frequency you'll need have some way to adjust the spring length, or pick up and shed weight on the fly, or something. If you drive it at resonance, the resonance will mean the motor doesn't have to do all the heavy lifting. Maybe you could even get away with a smaller motor.
PWM. Controllers for motors as beefy as the one in your picture typically use pulse-width modulation. Your linear setup with pot and transistors is attractively simple and intuitive. But consider that all the electric power that your motor isn't drawing will have to be dissipated as heat by those poor heat-sink-less transistors. A PWM setup, instead of dissipating the power, in effect turns it off for some fraction of the time, many times a second. It will be considerably more complicated, though -- probably including something like an Arduino. Keep those transistors, though, they might yet serve as the switching element.
Crank, or cam. (You only asked about the motor and controller, so this is just kibitzing.) A crank, shaped like the L-shape part that connects a bicycle pedal to the gears, would convert rotary motion from the gearbox shaft into up&down motion of the 5-pound decoration. If you drive it at mechanical resonance, the weight will bounce on the spring higher than just the crank throw. OTOH you might get interesting behavior by driving with a cam shaped to do something besides sinusoidal -- like a gradual rise followed by a sudden drop.