Primary methods for generating short pulses in lasers require intracavity elements or physical mechanisms for modulation or the saturable absorption of radiation. This often complicates laser design and limits capabilities, particularly beyond single-wavelength operation. We propose and explore a method for the synchronous generation of bicolor, high-repetition-rate pulses that combines stimulated emission from Yb rare-earth ions and Raman scattering in a shared all-fiber laser cavity, without employing saturable absorbers or modulators. The proposed mechanism for pulsed lasing is analogous to an optical shift register, with two pulse trains shifting relative to each other by one period after every round trip. This naturally solves the critical problem of compensating for the dispersion-induced differential delay of bi-chromatic pulses during an intracavity round trip. The shift register inherently enables stationary generation of bi-chromatic pulses with a common relatively high repetition rate that is inversely proportional to the differential delay. We have demonstrated the feasibility of the proposed technique through the stable generation of sub-nanosecond bi-chromatic (1066 and 1241 nm) pulses with a repetition rate exceeding 166 MHz. The proposed approach is rather general, and we anticipate that it can facilitate more affordable bi-chromatic pulse generation in a variety of laser systems.