Bat ears are not actually more significantly sensitive than human ones, they're just sensitive to another range of frequencies, or rather a wider range. That said, they may be bothered by sounds which we can in fact hear but don't consciously register as alarming.
You'd probably be best off putting up a really wideband condensor mic (e.g. Brüel and Kjær small-diaphragm type - they make quarter- and eighth-inch diaphragm jobs with response to 100kHz, though the noise floor suffers as the bandwidth goes up) and recording the output on something very broadband (e.g. 192kHz-sampled digital recorder) so that you can later analyse it for ultrasonic or other noise which may be disturbing them. If you can correlate the disturbance with something on the sound recording you're on to something. Some audio editing programmes, such as Adobe Audition, will display a waveform as a spectrogram, which is a fantastic way of trying to spot disturbances of all kinds. A noise meter, as such, is almost certainly too crude an instrument to pick anything up.
Once you've caught the sound and (let's suppose) located the bits of it that seem to agitate the bats, you can listen to it and try to work out what's causing it. Ear is far the best way of doing that part!
