Would it be a bad idea to get a tattoo over the scar I got from surgery?

Not really. In some cases, the tattoo may help to hide a unsightly scar. But generally, if you are not happy with a scar, you should have scar revision treatment.
Tattoo can cover it. I have seen some patients get a long tattoo along their tummy tuck scar. Looking closely, the scar is minimally noticeable. Since the tattoo extends beyond the scar, the observer's eye will tend to follow the outline of the entire tattoo rather than the scar. Beware that the scar within the tattoo may take the ink slightly different than than the adjacent skin, so plan on at least one touch up.