What is a bipolar capacitor and when is it used?

Bipolar is not commonly used these days (outside of psychiatric circles, of course). The more common term is unpolarized. This is in contrast with polarized capacitors such as electrolytics, where applying the wrong polarity can destroy the cap.

So a bipolar label is typically used to draw attention to a cap whose value is so large that a polarized cap might be expected, but which must not actually be polarized.

A bipolar capacitor is just a non-polarized capacitor. I think the term is usually in reference to a type of electrolytic capacitor to make it clear that you can use it in any orientation since they're usually polarized. I don't think they're otherwise special. At a high-level you could replace it with a ceramic capacitor of the same capacitance. The important part is that they seem to think it is important to use a non-polarized capacitor that is 100 uF. A ceramic equivalent would be pretty expensive if you could find it.

That said, unless they expect "ground" to go above the "input" I see no reason why you couldn't use a polarized electrolytic cap.