  We present u'g'r'i'BV photometry and optical spectroscopy of the Type Ib/Ic
SN 2005bf covering the first ~100 days following discovery. The u'g'BV light
curves displayed a double-peaked morphology, which is among Type Ib/Ic
supernovae. The bolometric light curve indicates that SN 2005bf was a
remarkably luminous event. Spectroscopically, SN 2005bf underwent a unique
transformation from a Type Ic-like event at early times to a typical Type Ib
supernova at later phases. The initial maximum in u'g'BV was accompanied by the
presence in the spectrum of high velocity absorption lines of Fe II, Ca II, and
H I. The photospheric velocity derived from spectra at early epochs was
unusually low compared with ordinary Type Ib supernovae. We describe
one-dimensional computer simulations which attempt to account for these
remarkable properties. The most favored model is that of a very energetic (2 x
10^{51} erg), asymmetric explosion of a massive (8.3 M_sun) Wolf-Rayet WN star
that had lost most of its hydrogen envelope. We speculate that an unobserved
relativistic jet was launched producing a two-component explosion consisting of
1) a polar explosion containing a small fraction of the total mass and moving
at high velocity, and 2) the explosion of the rest of the star. At first, only
the polar explosion is observed, producing the initial maximum and the high
velocity absorption-line spectrum resembling a Type Ic event. At late times,
this fast-moving component becomes optically-thin, revealing the slower-moving
explosion of the rest of the star and transforming the observed spectrum to
that of a typical Type Ib supernova. If this scenario is correct, then SN
2005bf is the best example to date of a transition object between normal Type
Ib/Ic supernovae and gamma ray bursts.
