Respondent-driven sampling (RDS) is a method for recruiting "hidden" populations through a network-based, chain and peer referral process. RDS recruits hidden populations more effectively than other sampling methods and promises to generate unbiased estimates of their characteristics. RDS's faithful representation of hidden populations relies on the validity of core assumptions regarding the unobserved referral process. With empirical recruitment data from an RDS study of female sex workers (FSWs) in Shanghai, we assess the RDS assumption that participants recruit nonpreferentially from among their network alters. We also present a bootstrap method for constructing the confidence intervals around RDS estimates. This approach uniquely incorporates real-world features of the population under study (e.g., the sample's observed branching structure). We then extend this approach to approximate the distribution of RDS estimates under various peer recruitment scenarios consistent with the data as a means to quantify the impact of recruitment bias and of rejection bias on the RDS estimates. We find that the hierarchical social organization of FSWs leads to recruitment biases by constraining RDS recruitment across social classes and introducing bias in the RDS estimates.