Bitterness comes from a continued holding onto the entitlements or prestige one expected one was due, but were thwarted by the actions of others or life circumstances.
Unfortunately, bitterness is a very ingrained emotion, built up over a long period of time. A person in this frame of mind would have closed themselves off from a lot of other opportunities, just so they can continue to have justification for what they feel. Typically, other people avoid triggering the emotions by avoiding the topic, as it can be very uncomfortable listening to bitterness and resentment talking.
So, how does one break the 'spell'? That will be difficult unless the one affected can disconnect from the circumstances that led to the original decision to feel aggrieved. Bitterness and resentment are there because of the continued decision that the original decision was valid, resulting in a lot more emotional investment.
If they can be brought to talk about the trigger point of the decision, but not so that they re-enter the thinking pattern, there may be a chance to dissipate some of the emotion, so that they may get to objectively see that that decision was invalid.
If their friends or loved ones cannot do that, a clinical psychologist could, but the person would have to be amenable to that. Otherwise, it would possibly take a heavy emotional shock of a more serious nature that would show them how much of life they had bypassed, but only life could arrange that.
We can get so caught up in the emotions that we carry as a result of our experiences that we may not see that what we wanted or expected was not what we really needed, but an addiction to our desires. Step 1 of breaking that is to stop reinforcing the beliefs, and step 2 is being willing to see the truth, both of the original circumstances, and what the beliefs have done to us. Step 3 is walking away from it all!