In order to trigger the quest, the player has to talk to Bittercup at the Big Towncommon house and be polite to her. Once she makes it clear she's interested in the player's character (gender is not an issue), responding that they are not in any relationship at the present will cause her to give the player miscellaneous items every 13 hours, selected at random from the following list:
The name of the quest is a modified phrase My cup runneth over, from Psalm 23:5, meaning that one has more than enough for their needs.
↑Fallout 3 Official Game Guide Game of the Year Edition p.351: "Head into the Common House and look for a morose young woman named Bittercup (check her schedule). She's grumpy, sarcastic, and her plan in life is to die by the light of the full moon surrounded by candles, while wearing her favorite black dress. Politely greet her. When she (finally) stops talking, reply that no one understands you either. After she lists every man she's dated in Big Town (well, except Shorty), reply that you have something to say. After her warbling, choose any of the first three responses. She hits on you. Respond by telling her you're not in any sort of relationship. She bashfully ends the conversation. Return to her once every 24 hours, and she gives you a very common, usually useless present, such as a Squirrel-on-a-Stick or Nuka-Cola Bottle. Thanks, lover! * Bittercup's low-quality Wasteland Junk"