A black hole does not have to remain in one place.
Many black holes begin as massive stars. Those stars are already moving through the galaxy. When one collapses, the black hole it leaves behind keeps moving. If the collapse is uneven, the black hole may also receive an additional push.
A black hole can be pushed much harder when it collides and merges with another black hole. It can also be thrown outward after a close encounter with other massive objects.
If that push is strong enough, the black hole can escape its star cluster or even its galaxy. It then travels through space without belonging to any particular system.
Space has almost nothing in it to create resistance. There is no air to slow the black hole down. Unless the gravity of another object changes its path, it will continue moving in the same general direction.
Some runaway black holes can travel at thousands of kilometres per second. The highest speed predicted from a black-hole merger is about 5,000 kilometres per second. At that speed, a black hole could cover the distance between Earth and the Moon in a little over a minute.
That sounds close to the speed of light, but it is not.
Light travels almost 300,000 kilometres every second. A black hole moving at 5,000 kilometres per second is travelling at less than two per cent of light speed. We have never observed a black hole moving anywhere near light speed.
Could one reach us?
Yes, in the strictest sense. A black hole could travel through the Solar System. If it passed close enough, its gravity could alter the orbits of the planets. Earth might be pushed into a different orbit, pulled away from the Sun or destroyed during an extremely close encounter.
The black hole would not need to swallow us.
Such an encounter could become destructive very quickly once the black hole was nearby. But it would not cross the galaxy in an instant. Even at 5,000 kilometres per second, travelling just one light-year would take about sixty years.
The Milky Way may contain around 100 million isolated black holes. That number sounds alarming until the size of the galaxy is considered. The distance between these objects is usually measured in light-years, while the Solar System is a very small target.
So the possibility is real, but the danger is remote. Black holes can travel alone. Some move extraordinarily fast. One could, in principle, pass near Earth.
What is not supported by evidence is the idea of a black hole travelling near the speed of light and suddenly reaching us before anything could be noticed.
Sources: NASA on isolated black holes, research on black-hole recoil speeds, and JWST observations of a runaway supermassive black hole.