Source bearing estimation is a common application of linear sensor arrays. The Cramer-Rao bound (CRB) sets a lower bound on the achievable mean square error (MSE) of any unbiased bearing estimate. In the spatially white noise case, the CRB is minimized by placing half of the sensors at each end of the array. However, many realistic ocean environments have a mixture of both white noise and spatially correlated noise. In shallow water environments, the correlated ambient noise can be modeled as cylindrically isotropic. This research designs a fixed aperture linear array to maximize the bearing Fisher information (FI) under these noise conditions. The FI is the inverse of the CRB, so maximizing the FI minimizes the CRB. The elements of the optimum array are located closer to the array ends than uniform spacing, but are not as extreme as in the white noise case. The optimum array results from a trade off between maximizing the array bearing sensitivity and minimizing output noise power variation over the bearing. Depending on the source bearing, the resulting improvement in MSE performance of the optimized array over a uniform array is equivalent to a gain of 2-5 dB in input signal-to-noise ratio.