Due to the polarization sensitivity of Raman gain and the random nature of polarization mode dispersion (PMD) in the fiber, the gain of a fiber Raman amplifier (FRA) fluctuates over a wide range during a relatively long time. In this work, a numerical method of obtaining the probability distribution function of the random fluctuating Raman gain in a bidirectionally pumped FRA is presented for the first time, based on the vector theory of stimulated Raman scattering (SRS). After optimizing a bidirectionally pumped FRA to achieve the best tradeoff between an optical signal-to-noise ratio (OSNR) and nonlinear distortions, the proposed method is applied to study the impact of gain fluctuations. The results show that the fluctuations reach their peaks at two values of PMD parameters (Dp), respectively, when Dp is increased from zero. The heights of the two peaks are proportional to the power allocations for the forward and backward pumps, respectively. The results are useful for avoiding high gain fluctuations when bidirectional pumping is applied.