What areas of the bat brain are involved in echolocation and how do they process these signals?

Answer 1

Like in the human brain, hearing is processed in the auditory cortex of the temporal lobe. However, making sense of the sounds received is handled in other parts of the temporal lobe as well as associative areas of the parietal lobe.

Here's a wiki article that gives more specifics about signal processing and cell groups involved:
http://en.wikipedia.org/wiki/Animal_echolocation

Answer 2

In addition to the areas described by Mera, some parts of the cerebellum are also involved.