Recently, a range-Doppler map-based direction-of-arrival (DOA) estimation method was proposed for amplitude modulation (AM) radio-based passive bistatic radar (PBR). This method estimates the incident angle from the phase difference of the range-Doppler-bin (RD-bin) for the specific bistatic range of the cross-ambiguity function (CAF) and the Doppler frequency value rather than the phase difference between each antenna signal. In particular, in AM radio-based PBR, the RD-bin-based signal processing technique was adequately used to transform the range dimension of the CAF into an angular dimension. In this study, we improve the RD-bin-based DOA estimation method for frequency modulation (FM) radio-based PBR. The two main contributions of this paper are as follows. First, we present a criterion for deciding on the number of RD-bins using theoretical analysis. Second, we suggest that other target signals may become interference signals in the presence of multiple targets, which may degrade the DOA estimation accuracy. We also propose a least-squares-based algorithm to solve this problem. From the simulation results, we show that the proposed criterion for deciding on the number of RD-bins is appropriate for FM radio-based PBR and that the proposed least-squares algorithm successfully removes the target interferences.