Once you have been to Little Lamplight, you have the option to talk to Eulogy Jones about it. He voices his opinion on child slaves being good for business and commissions you to kidnapping a kid for him. Return to Little Lamplight and search for an appropriate kidnapping candidate.
Most of the kids are old enough to know what is happening and avoid your inquiries entirely. However, Bumble is the youngest child in Little Lamplight and will naively follow you if you pass a Speech check or use the Child at Heart perk to convince her. A child slaver waiting outside gives Bumble a pretty necklace and takes her to Paradise Falls (which sounds like a nice place to Bumble). Eulogy Jones rewards you with the Boogeyman's hood.
It's quite possible to lure the child slaver out to kill her by bringing Bumble out from the caverns. This does not seem to make other Slavers hostile towards you. You also suffer no Karma loss, since the necklace is never placed on Bumble. "I don't like outside. I'm going home", Bumble will say and return to the caverns.
Once Bumble and the child slaver reach the child slave house in Paradise Falls, both are disabled and disappear from the game.
No karma is lost for completing this quest.
PCPlayStation 3Xbox 360 After this unmarked quest is complete, you can inquire to Eulogy about enslaving children again, which will have Bumble respawn in Little Lamplight with a slave collar on, but no child slaver will be waiting.