The thing is, they do have speed. At least in comics (I'm not talking TV shows or movies).
Comic Book Peak Humans and people edging into that range have a long, laundry-list of speedfeats that are simply impossible for real-world humans to replicate. They are explicitly superhuman by our real-world standards.
Their handspeed is invisible, their whole-body movements are nothing but a blur.
They casually and consistently catch multiple arrows from the air, sometimes behind themselves. Sometimes they even do it by reverse-Robin-Hood - catch one arrow, stop the second one by sticking the first one in the way so that the second one splits it down the middle. While chatting.
They blitz groups of a dozen or more normals and take them all out in a bare few seconds.
Given that Batman would be nothing more than a dark blur to normals, a dark blur moving so quickly that people simply can't keep up that is also laying down explosives, flash-bangs, smoke, and throwing knives while he moves, it's hardly surprising that people trying to track him fail utterly. Or hit all of that armor he wears, rather than his chin.
Movies do a pretty poor job of showing this, of course.
Is it silly that Batman has managed this sort of thing for decades and decades without taking one bullet in the face? Sure - odds get kind of long after a point. But the idea behind it is not. The idea is really no more silly than dudes who can turn to steel, or shoot laser beams from their eyes, or control magnetic force and electromagnetic energy with their mind.