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We report the synthesis of CeBi single crystals out of Bi self flux and a systematic study of the magnetic and transport properties with varying temperature and applied magnetic fields. From these $R(T,H)$ and $M(T,H)$ data we could assemble the field-temperature ($H-T$) phase diagram for CeBi and visualize the three dimensional $M-T-H$ surface. In the phase diagram, we identify regions with well defined magnetization values, and identify a new phase region. The magnetoresistance (MR) in the low temperature regime shows, above $6~$T a power-law, non-saturated behavior with large MR ($\sim 3\times10^5 \%$ at $2~$K and $13.95~$T), along with Shubnikov-de Haas oscillations. With increasing temperatures, MR decreases, and then becomes negative for $T\gtrsim 10~$K. This crossover in MR seems to be unrelated to any specific magnetic or metamagnetic transitions, but rather is associated with changing from a low-temperature normal metal regime with little or no scattering from the Ce$^{3+}$ moments and an anomalously large MR, to an increased scattering from local Ce moments and a negative MR as temperature increases.