Are you wanting pure black and white (no grey) or greyscale?
If you just want greyscale, you can set the saturation all
the way down. Then, you might want to experiment with the
brightness and contrast, since de-saturated color images tend to
look muddy...it depends on the content.
A greyscale image will have only 256 shades in it, and you
can safely save that as a gif without the color getting off or any
other JPEG noise artifacts being introduced.