According to this website (which references all of Moogs patents), the Bode frequency shifter is a ring modulator with the lower sideband suppressed. Another name for this effect is a single side band ring modulator.
There is an already-built example of this in the Modulation category of the Prototypes called SingleSideBandRM. Double-click on the icon in the Prototypes window, select the second icon from the right and choose Describe Sound from the Info menu to get a description of the Sound and how to use it.
-- KurtHebel - 09 Jan 2005
Has this the one been updated to use the All frequencies unity gain 90 deg phase shifter, or is it only a true single sideband ring modulator at one center frequency as it was in the old Prototypes ?
-- PeteJohnston - 10 Jan 2005
The prototype uses an all pass filter to get the 90 degree phase shift (which may be similar to what the old analog circuitry did), so it does exact frequency shifting in the vicinity of the Frequency parameter's value.
The Hilbert transformer can do a wider bandwidth of 90 degree phase shifting and so would give a more accurate frequency shift. On the telephone, Pete was mentioning that he thought there may be an example of this kind of frequency shifter (using an FIR filter as the Hilbert transformer) in the Kyma Forum.
-- KurtHebel - 10 Jan 2005