You can't get any farther from feeling real pain than to take other people's money under the pretense of relieving their pain. Not that anyone who would actually fall for this scam is capable of dealing with real pain in any case. And you certainly can't get any farther from feeling real pain than by sucking up to other people's pain in hopes that it will obliterate your own. There's no bitterness in bittersweet anyway. Bittersweet is for chocolate.
Real bitterness has an equal component of rage.
Go listen to Shostakovich. Try the 8th symphony, in which he batters you with violence and anguish for 45 minutes, then lets you feel a glimmer of hope, and finally crushes that hope with a tank. Try the second piano trio, which ends with Jews being forced to dance on their graves before being shot. Try the 9th symphony, which was to be a grand celebration of Russia's victory over Germany. That was his celebration, laid on the line in concert for an audience of Stalin and his generals.