The Kid-Kidnapper

 refers to an unmarked quest in Fallout 3.

Once you have been to Little Lamplight, you have the option to talk to Eulogy Jones about kidnapping one of the children there which in turn nets you this assignment. Convince Bumble in Little Lamplight to follow you to the Child Slaver waiting outside, either by passing a Speech check or by using the Child at Heart perk.

Reward
Eulogy Jones rewards you with the Boogeyman's hood.

Bugs

 * If the Child Slaver is killed while waiting outside by an enemy, like a Giant Radscorpion, you will not have the option for the speech check when talking to Bumble and you cannot get Eulogy to send another slaver, so this side quest becomes impossible.
 * After Bumble is taken by the Child Slaver outside of Little Lamplight and you've talked to Eulogy Jones and received the Boogeyman's hood, if you talk to Jones again about luring a kid out of Little Lamplight, she will reappear in Little Lamplight still wearing the slave collar. You can lure her outside again, where the Child Slaver will again be waiting. However, the dialogue between the two will not unfold as it should and they will stand there indefinitely.
 * A variation of the above, Bumble returns but the Child Slaver does not. If you convince her to follow you outside again she will follow you everywhere until you fast travel.
 * This also can be accomplished by luring Bumble outside, letting her begin to walk up to the slaver (beginning of scripted animation), then entering VATS and killing the slaver before Bumble fully runs away. She will follow you after fast traveling as well, but will immediately start fleeing if any enemies are even in the same cell (high perception). It is possible to reverse pickpocket her, but if detected she will start to flee and cower - but will oddly still follow you for a short period of time. She is categorized as an "enemy" on your radar, and will cause townspeople to flee.
 * If you agree to lure a kid out of Little Lamplight, it may cause Eulogy Jones to disappear from Paradise Falls. In the PC version you can recover him by following this guide.
 * Jones has also been known to disappear with both of his slaves for no reason at all.
 * Note: Sometimes he goes into the clinic owned by Cutter or other buildings and he and his slaves will get stuck in a space. Search around these buildings if you can't find him after completing the quest.
 * Also, he occasionally goes out onto the balcony above the entrance to his apartment. It's hard to see him up there as you enter, so its easy to miss him
 * Occasionally on 360 when you enslave Bumble she will later return to the cavern and you can tell her to go with the slaver as much as you want for the hood and unlimited money.
 * Occasionally when you lure Bumble outside, she will talk to the slaver and if you interrupt by talking to bumble, she will say 'see ya later' and just stand there waiting and the slaver will ask you for the child.
 * If you fail to talk Bumble into coming outside the first time then you might not have another chance to get her outside. Make sure you have the Perk, Child at Heart before you talk her into coming outside.
 * If you fast travel back to Paradise Falls and manage to "catch" the Child Slaver and Bumble en route (inside the city), they will get to the Slave Pen but will stay in the front of the gate indefinitely unless you have the key to unlock it.