(The following is based on some quick calculations that I did, assuming the mass of the SBH is exactly 1 million times the mass of the Sun.)
Now suppose that this SBH happened to come into our galaxy, and in fact came close to our solar system. (Again, this is so improbable as to be hardly worth considering. But it's still fun to think about.) Once it started moving through the Galaxy, we would start to notice the orbits of stars that it encountered being disrupted. And in fact, our solar system's orbit around the center of the Galaxy would be disrupted if it came close. How close? I'm thinking that we would start to notice something was fishy if it came within about 1000 light years of our solar system. But the disruption of our solar system's orbit around the galactic center probably wouldn't have any catastrophic implications for life on Earth. In fact, even if we were on a "collision course" with the SBH, we would probably have a few hundred thousand years between the time we cross that ~1000 ly threshold and the time the *real* disaster begins.