How can I achieve a very bitter flavor using the French press? I'm trying to train my tongue to recognize the 'bitter' taste of coffee, so I can improve my methods.  

How can I achieve a bitter flavor with a French press?

This is a real question as I am not sure if it is heat, steep time, or the coffee grounds that produce the bitterness.
Bitterness comes from over-extracting the coffee. The factors affecting extraction are: water temperature, time, size of the grind, and to a lesser extent, agitation.

Using hotter water (above the usual 198F-202F), longer steep time, or a finer grind--or any combination of the three--will result in over-extraction, which will make the coffee more bitter. A darker roast will over-extract more easily as well, since an ideal extraction is typically 30-45 seconds shorter than a light roast.