Given the mysterious boom today in San Diego, I started wondering what a sonic boom would look like to a bat. Remember that a bat sees with what amounts to a strobe effect (sonar does not return continuously) and its resolution horizon is around 17 meters. Some time ago I posted about faster-than-light travel, and specifically how it would look to a distant observer. Even if we can't imagine how to achieve faster-than-light travel, we might ask what it would look like from a long way off, and then look for those signs. It turned out someone had asked the same question rigorously.
So how would a supersonic object look to a bat? It's actually not that earth-shattering. If a supersonic object is moving is moving directly away from the bat, the bat would see nothing. The object would always out-race the soundwaves.
For all other situations, it depends on the angle between direction of observation and direction of forward motion of the object at the moment the sonar waves reflect from the object. There is nothing special about its being supersonic, although with such a small field of vision, the bat would miss most of its chances to sound off the object. Even with a barely supersonic object that cooperated by flying immediately past the bat without hitting it, if the bat were lucky enough to have a sonar wave reflect off the object just as it entered the bat's range, the bat would only be able to sound it when it was just past it. A faster object would already be past it; twice as fast as sound, and the bat would only be able to see one (accidental) glimpse of it. Of course this assumes an instantaneously reacting bat, whereas in the real world, neither nerve conduction velocity nor process times are zero. Realistically the bat would only see it once, with an impressive Doppler shift. Maybe the bat would regard it as a glitch (a hallucination) and ignore it.
Of course once the source of a wave outpaces the propagation of the wave, there are other effects - the boom. Though there are frequency differences in booms based on how much faster than the speed of sound they craft is going as well as the shape of the craft, none would really matter in terms of affecting the bat's perception in an organized way. It would be like a blinding flash of light to an animal that relies more on sensing electromagnetic radiation like we do.