Does a good hand washing suffice, or do I need to take additional action for a minor bite?

For a minor bite, a good hand washing with unscented soap and thoroughly rinsing would usually be sufficient. You can then protect the wound with a bandage. It is important to seek medical attention if the bite is near the eyes, if you have specific health issues like diabetes, a weakened immune system, or circulation problems, or if there are signs of infection such as redness, spreading affected area, discharge (white or colored), inflammation, pain, or warmth.