A black hole crossing our path would give plenty of warning, assuming it approaches significantly slower than the speed of light.

The effect of a black hole's gravity on distant objects is exactly the same as the effect of any other object with the same mass. It would disturb Kuiper belt objects that everyone's watching very carefully these days, affect the orbits of the outer planets as it moves closer, and bend light around its event horizon in a very obvious way.

Whether we can do anything about it, of course, is a different problem.