Basically there are three main sensors in use in current portable bat detectors. However new types of sensor are under development, and we may soon see some changes!
These are made for hearing aids. Although the manufacturers usually
dont specify how they respond above audio frequencies (i.e. above 20kHz), they can
be effective up to 100kHz and beyond, depending on the type used. They are very small,
robust and cheap. The sensor shown here is a miniature electret microphone insert,
with a diameter of about 5mm. Hearing aid microphones are even smaller.
These are crystal microphones, designed mostly for intruder detection. They
have a very narrow bandwidth, peaking at 38kHz, 40kHz, 45kHz or 50kHz. This means that
although they will pick up sounds from some bats such as pipistrelles, they will not pick
up other bats whose calls are outside their range of frequency. They are extremely cheap,
quite robust and produce a large signal output. There is considerable discussion
about their suitability for various types of bat detector, but my experiments indicate
that they are unsuited to wide band applications. (See graph below)
Purpose-made for bat detectors, usually by the manufacturer of the detector. They require
high voltages (typically 400V) which tends to limit battery life. They are not very
sensitive, so high gain, low noise & expensive amplifiers need to be used. They are
not very robust, so need care in handling. This can be a problem when its pitch black and
you are walking through a wood!
Polaroid make ultrasonic capacitance sensors for range finding applications and these can
also be used.
As I have already said, piezo transducers have serious limitations. Here is a graph of the frequency response of a 40kHz piezo transducer. You can see that the signal level is 20dB lower outside the 35 - 45 kHz range. Not much good for horseshoe bats! However the sensitivity of an electret microphone in the region from about 35 - 50 kHz can be greatly improved by adding one or two piezo sensors.

I'm told that the bandwidth of this type of detector can be extended by connecting a coil across the terminals. Tony Messina (see my links) says "Try using a Maplin HY12N ( the receiver ) paralleled with a 12 mH coil, and you will see what I mean" Bertrik Sikken also has some information about this on his website.