In a systematic viewpoint, bistability refers to the existence of two stable equilibriums for a biological system. But, I don't understand the difference between bistability and bimodality. In both cases, the system should have two different behaviors, so I guess bistability is a specific case of bimodality, in which either of the system's behaviors might not be stable. Is this a valid distinction between these terms?
Bistability referrers to two coexisting stable conditions (if you disrupt they will tend to restore to one of those two areas) and has a slightly broader application it can also involve chemical stability for instance. Bistability includes the element of stability (obvious in the name) if disrupted bistable condition tend to return to one of two stable configurations. Enzyme stable configurations could be another. Galapagos finch beak shape during wet years is the one I think of but that could also be argued as tri-stable. to go really simple you can even think of a clicky pen, fully clicked is stable and unclicked is stable but anything else immediately moves to one of the other states.
Bimodal just means the distribution has two peaks, they may or may not be stable, many are only temporary. It is a much simpler concept.
Another way to consider it is bimodal is purely descriptive while bistability has a predictive quality.