I get a bitter taste in my mouth after eating and even after just brushing my teeth. What causes this? I also have mucus in my throat but am not sick

Contradictory. You say you have a bad taste, and have a mucous problem, but that you are not sick. How long has it been since your last Dental examination and physical examination? Have you been evaluated for sinusitis, periodontal disease, GERD, diabetes, draining dental abscess, etc. How long has it been since your last professional cleaning? Do you floss or just ignore cleaning 35% of your tooth structures? .
Gum disease. Bitter taste can be a sign that you are at risk for, or already have, gum disease. The bacteria, along with mucus and other particles, constantly form a sticky, colorless toxic “plaque” on teeth causing the gums to become inflamed and to easily bleed. This condition should be checked by a dentist. It is a painless condition, but can induce serious complication.