Are you trying for genuine black and white or a grey scale just shifted so the grey tint becomes white?
In a home context I've found telling the scanner driver to scan black and white or grey scale and do a two pass scan to set the threshold works well.
I think even the built-in Windows paint will talk to a scanner if the driver is installed.
It can be done in Photoshop using levels but it's very fiddly. GIMP is bound to have an equivalent, and I think paint.net does too (and is much easier to get started with).
I did once automate a black and white workflow using Imagemagick but the requirement there was fast and cheap, not quality.