In this paper, we study a feedback bit allocation algorithm with signal-to-leakage plus noise ratio maximizing beamforming (FA-SMB) for distributed antenna systems (DAS) presented in work . We first investigate a scaling law of feedback bits for both the FA-SMB scheme and equal bit allocation. Through this analysis, we confirm that the required number of feedback bits to satisfy the maximum allowable rate gap between DAS with perfect channel state information (CSI) and limited feedback linearly increases with signal-to-noise ratio. Also, it is verified that the FA-SMB scheme saves the feedback bits by up to 30% over the equal bit allocation with the same rate gap at SNR = 40 dB for three-user DAS. Moreover, we show that the FA-SMB scheme substantially reduces the computational complexity compared to exhaustive search. Finally, we provide simulation results to demonstrate the efficacy of the FA-SMB scheme.