The spread of sexually transmitted diseases (e.g., chlamydia, syphilis, gonorrhea, HIV, etc.) across populations is a major concern for scientists and health agencies. In this context, both the data collection on sexual contact networks and the modeling of disease spreading are intensive contributions to the search for effective immunization policies. Here, the spreading of sexually transmitted diseases on bipartite scale-free graphs, representing heterosexual contact networks, is considered. We analytically derive the expression for the epidemic threshold and its dependence with the system size in finite populations. We show that the epidemic outbreak in bipartite populations, with number of sexual partners distributed as in empirical observations from national sex surveys, takes place for larger spreading rates than for the case in which the bipartite nature of the network is not taken into account. Numerical simulations confirm the validity of the theoretical results. Our findings indicate that the restriction to crossed infections between the two classes of individuals (males and females) has to be taken into account in the design of efficient immunization strategies for sexually transmitted diseases.