Bitterness is an reaction to the bite of venom from satan. The old testament reaction that is. The new testament reaction does not include bitterness but doesn't exclude the pain from the bite. Bitterness of the Old testament isn't the same as Christians are meant to experience in the New Testament.
The old testement refers to "the angry discontent of a rebelious person" resulting from the "poison venom of the serpent".
Look at these results from a search of Strong's Concordence on the word bitter or bitterness in the Hebrew
4751 mar mar or (feminine) marah {maw-raw'}; from 4843; bitter (literally or figuratively); also (as noun) bitterness, or (adverbially) bitterly:--+ angry, bitter(-ly, -ness), chafed, discontented, X great, heavy.
4805 mriy mer-ee' from 4784; bitterness, i.e. (figuratively) rebellion; concretely, bitter, or rebellious:--bitter, (most) rebel(-lion, -lious).
4846 mrorah mer-o-raw' or mrowrah {mer-o-raw'}; from 4843; properly, bitterness; concretely, a bitter thing; specifically bile; also venom (of a serpent):--bitter (thing), gall.
There are other references in the OT but these are the usual meaning. There is, however, only 4 meanings for the same words in the NT.
When bitterness is spoken of in the NT believer it refers to a bitter and violent piercing and makes no mention of anger, discontent or rebellion.
Results in Greek
4087. pikraino pik-rah'-ee-no from 4089; to embitter (literally or figuratively):--be (make) bitter.
4088. pikria pik-ree'-ah from 4089; acridity (especially poison), literally or figuratively:--bitterness.
4089. pikros pik-ros' perhaps from 4078 (through the idea of piercing); sharp (pungent), i.e. acrid (literally or figuratively):--bitter.
4090. pikros pik-roce' adverb from 4089; bitterly, i.e. (figuratively) violently:--bitterly.
Satan can still bite the new creation of believers, sometimes using those closest to us to inflict the pain. But ....
Jesus' saving grace saves us from the anger, discontent and rebellion but not from the pain involved from the poison inflicted on tender hearts, made more tender from association with Jesus. Jesus' compassion always shone through His pain, but no doubt Satan inflicted serious poison on His soul, probably more than any other.
It also helps to see and prove Christ's overcoming to the new creation