The most general feeling of sorrow or unhappiness can be captured with the adjective sad. The word bitter, on the other hand, describes a more pointed feeling, often one of disappointment, sharpened by resentment, hostility, or cynicism. A bitter sorrow is one that is deeply grievous or hard to bear. A bitter lesson is one that is hard to accept. And bitter rivals are competitors whose relationship is marked by intense antagonism or hostility. In all of these, you can find traces of bitter's earliest sense in English: "having a harsh or disagreeable taste."