We report extensive radio and X-ray observations of SN 2003bg whose spectroscopic evolution shows a transition from a broad-lined Type Ic to a hydrogen-rich Type II and later to a typical hydrogen-poor Type Ibc. We show that the extraordinarily luminous radio emission is well described by a self-absorption dominated synchrotron spectrum while the observed X-ray emission at t~30 days is adequately fit by Inverse Compton scattering of the optical photons off of the synchrotron emitting electrons. Our radio model implies a sub-relativistic ejecta velocity, v ~ 0.24c, at t_0 ~ 10 days after the explosion which emphasizes that broad optical absorption lines do not imply relativistic ejecta. We find that the total energy of the radio emitting region evolves as E ~ 7.3 x 10^{48} (t/t_0)^{0.4} erg assuming equipartition of energy between relativistic electrons and magnetic fields (e_e=e_B=0.1). The circumstellar density is well described by a stellar wind profile with modest (factor of ~2) episodic density enhancements which produce abrupt achromatic flux variations. We estimate an average progenitor mass loss rate of M_dot ~ 3 x 10^{-4} solar masses per year (assuming a wind velocity of 1000 km/s), consistent with the observed values for Galactic Wolf-Rayet stars. Comparison with other events reveals that ~50% of radio supernovae show similar short timescale flux variations attributable to circumstellar density irregularities. Specifically, the radio light-curves of SN 2003bg are strikingly similar to those of the Type IIb SN 2001ig, suggestive of a common progenitor evolution. We conclude that their progenitors experienced quasi-periodic mass loss episodes just prior to the SN explosion. [ABRIDGED]
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