The ability of a user to upload and compare samples online seems a very useful idea.

Perhaps the unique calls of individual bats will be detected in multiple locations showing the range of these interesting mammals.

Modelling the ability of a horn fed microphone to detect low amplitude sounds is not currently on the agenda buy I am concerned the sensitivity of this may not be enough.  Having a cute looking detector that leverages the processing and sensors of a smartphone for logging is good but if the microphone concentrators shapred as ears result in the device being too directional that may reduce the ability of the detector to detect and identify bat calls.

P.S.  Perhaps the case could be covered in a soft foam to damp vibrations from the user while it is being held?

In this use case which I imagine is the most common then the design of the case for handheld use deserves detailed attention.