Feasibility of custom parabolic mic (amplified, bandpass filtered) for use with mobile phone app
You have several problems if you want to power your amplifier and filter through just the bias for the electret microphone.


Voltage.  You've already mentioned this.  There's only a couple of volts available as bias for the microphone on your cellphone.  There are amplifiers that can operate on just a couple of volts, but they are rarer and more expensive than your run of the mill operational amplifier.
Current.  Besides the voltage, the available current is limited.  There's typically a resistor of around 2000 ohm resistance in line with the bias.  You get like 1 milliampere of current that you can use.
You have to share the available voltage and current between your amplifier/filter and the microphone.


The solution is simple:  

Don't bother.  

Use a small battery to power an amplifier, the filter, and the microphone.

You have to build something to hold the microphone and the dish together.  Just go ahead and make the handle large enough to hold a 9V battery (or other small battery.)

Find online calculator for a sallen-key bandpass filter and give it your frequency limits.  It will suggest a circuit and a set of part values that will approximate your requirements.

Use that as your filter.

Use a simple op-amp amplifier for gain (to make it louder.)

Power it from your battery, and pack the whole shebang in the gadget you use to hold your microphone and dish.

A resistor is series with the output will take care of things if you are worried about your phone's microphone input.  Shouldn't be a problem, though, as op-amps don't provide a lot of current.



Instead of a dish, you might consider one of these.  

That link goes to a DIY  "shotgun" microphone.

It looks like this:



That one covers a large range of audio frequencies.

The pipes are of various lengths to resonate at different frequencies.

If you make it using just lengths corresponding to the frequencies you are interested in, then you get your bandpass filter implemented acoustically.

You can still use an electronic filter with it, of course.  And an amplifier.

Using just the frequencies you mentioned will make the whole thing shorter - more of a "shot-pistol" than a "shotgun."



Something else you should consider:

If you want to record the critters, then you may be able to get by without any special hardware.  

Record using an uncompressed file format (.wav or aiff instead of .mp3 or .ogg)  Use a high sampling rate, and 16 bit samples 

You can then use a program like Audacity to filter and amplify the chirps.

You can gain a lot of volume that way.

There may be programs that let you do all of that live, on your phone.



The module you linked to is probably a very good start.  It has plenty of gain (amplification) and will lower the gain if the sound is too loud.

The microphone loses maybe 3 dB from 10kHz to 20kHz.  You would be hard pressed to notice the difference.  Consider the loss of 3dB (factor of 0.5) as compared to the gain (60dB, factor of 1000.)  The little bit of loss doesn't really matter