Bitterness in people is caused by very great disgust, it is a deeper and more complex reaction than just a momentary expression of anger.

Bitterness is a satanic fortress which must be faced with all frankness.
Hebrews 12:15, lest any man fail to attain the grace of God, that by sprouting some root of bitterness, he shall trouble you, and by it many shall be defiled.
An angry person is easy prey to reach bitterness if this, does not practice what the Lord commands, that the sun does not set on your anger.
Time makes the difference between anger and bitterness, anger being a momentary expression on your face or even body, but the bitterness remains in the heart.
That is why God reminds us that we must guard our hearts because life flows from him.
So if you have trouble dealing with bitter people, just cry out to God and you can get the victory, God is calm in the midst of storms.