We investigate coordinated regularized zero-forcing precoding for limited feedback multicell multiuser multiple-input single-output systems. We begin by deriving an approximation to the expected signal-to-interference-plus-noise ratio for the proposed scheme with perfect channel direction information (CDI) at the base station (BS). We also derive an expected SINR approximation for limited feedback systems with random vector quantization (RVQ) based codebook CDI at the BS. Using the expected interference result for the RVQ based limited feedback CDI, we propose an adaptive feedback bit allocation strategy to minimize the expected interference by partitioning the total number of bits between the serving and out-of-cell interfering channels. Numerical results show that the proposed adaptive feedback bit allocation method offers a spectral efficiency gain over the existing coordinated zero-forcing scheme.