It helps to think of the bias-variance trade off in terms of the hypothesis space. Dropout trains subnetworks at every iteration. The hypothesis space of the full network will always contain (and be larger) than the hypothesis space of any subnetwork, because the full network has greater expressive capacity. Thus, the full network can not be any less biased than any subnetwork. However, any subnetwork will have reduced variance because of its smaller relative hypothesis space. Thus, dropout helps because its reduction in variance offsets its increase in bias. However, as the dropout proportion is set increasingly higher, eventually the bias will be too great to overcome.