Determining sensor bandwidth
Imagine a plate moving back and forth sinusoidally in front of your sensor.  If the bandwidth of the sensor is much greater than the frequency of the motion, then the output of your sensor will track the motion very well.  

For example if the output sensitivity is 1 V per meter, and your plate is moving +/- one meter, your sensor will put out a +/- 1 V sinusoidal signal.

Now, if the plate is moving back and forth at the bandwidth of the sensor, even though the plate is still moving +/- 1 meter, the output of your sensor will put out 3 dB less, or +/- 0.707 V.  

If the plate is moving much faster than the bandwidth of the sensor you would see only a very small signal on the output.

So the sensor bandwidth is a measure of the ability of the sensor to follow changes in the sensed quantity.

As to the lack of data in datasheets the only advice is caveat emptor.  If your design depends on anything that's not specified, (and not just as a typical spec) you are rolling the dice.